Course: 11.11 使用结果或概率计算奇数

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使用结果或概率计算奇数
When you think about chances and odds, you can calculate the likelihood that an event will occur or not occur.
::当你想到机会和机会时,你可以计算出事件发生或不发生的可能性。

Jamie was listening to the weather forecast to determine if he and his friends should go to the beach. The weather forecaster said that there was a 4 in 5 chance of showers. What is the chance that he will be going to the beach with his friends? How can Jamie express his odds as a fraction and a percent?
::Jamie在听天气预报以确定他和朋友是否应该去海滩。天气预报员说,每5次有4次机会淋浴。他和朋友去海滩的机会有多大?Jamie如何能以分数和百分数来表达他的几率呢?

In this concept, you will learn to calculate odds by using outcomes or probability .
::在此概念中,您将学会使用结果或概率来计算概率。

Outcomes
::成果成果成果

The probability of an event is defined as a ratio that compares the favorable outcomes to the total outcomes . This ratio can be expressed in fraction form.
::事件的概率被定义为将有利结果与总结果进行比较的比率。这一比率可以分数表示。

$\begin{aligned} P (event) = \frac{# of favorable outcomes}{total # of outcomes} \end{aligned}$
$\begin{align*}P \text{(event)} = \frac{ \# \ \text{of favorable outcomes}}{\text{total } \# \ \text{of outcomes}}\end{align*}$
::P(活动)++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++#######++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++################+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++#

Sometimes people express the likelihood of events in terms of odds rather than probabilities. The odds of an event occurring are equal to the ratio of favorable outcomes to unfavorable outcomes .
::有时,人们用概率而不是概率来表达事件发生的可能性,事件发生的可能性相当于有利结果与不利结果的比例。

$\begin{aligned} (odds) = \frac{# of favorable outcomes}{unfavorable # of outcomes} \end{aligned}$
$\begin{align*}\text{(odds)} = \frac{ \# \ \text{of favorable outcomes}}{\text{unfavorable} \ \# \ \text{of outcomes}}\end{align*}$
:ods) +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++#++++++++++++++####+++++++++++++++######++++++++++++######++++++++++++++++++++++++++++++++++++############+++++++++++++++++++++++++++++++++++++++++

Think about the odds for the arrow of the spinner above landing on red:
::想想在红色上着陆的旋翼箭头的几率:

Favorable outcomes = 1 (red)
::有利结果=1(红色)

Unfavorable outcomes = 2 (blue, yellow)
::不利结果=2(蓝色、黄色)

Total outcomes = 3

::总结果=3

So the probability of spinning red is:
::因此,旋转红色的概率是:

$\begin{aligned} \begin{array}{rcl} P (red) & = & \frac{# of favorable outcomes}{total # of outcomes} \\ P (red) & = & \frac{1}{3} \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} P \ \text{(red)} &=& \frac{\# \ \text{of favorable outcomes}}{\ \text{total # of outcomes}} \\ P \ \text{(red)} &=& \frac{1}{3} \end{array}\end{align*}$
::P(red)++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++13++++++++++++++13+++++++++++13+++++++++++++++++++++++++++++++13++++++++++++++++++13+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

While the odds in favor of red are:
::红色的胜算是:

$\begin{aligned} \begin{array}{rcl} odds (in favor of red) & = & \frac{# of favorable outcomes}{# of unfavorable outcomes} \\ odds (in favor of red) & = & \frac{1}{2} \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \text{odds} \ \text{(in favor of red)} &=& \frac{ \# \ \text{of favorable outcomes}}{\# \ \text{of unfavorable outcomes}} \\ \text{odds} \ \text{(in favor of red)} &=& \frac{1}{2} \end{array}\end{align*}$
:赞成红色) +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++12+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Odds against an event occurring are defined as:
::针对发生的事件的奇数的定义如下:

$\begin{aligned} \begin{array}{rcl} odds (against red) & = & \frac{# of unfavorable outcomes}{# of favorable outcomes} \\ odds (against red) & = & \frac{2}{1} \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \text{odds} \ (\text{against red)} &=& \frac{ \# \ \text{of unfavorable outcomes}}{\# \ \text{of favorable outcomes}} \\ \text{odds} \ (\text{against red)} &=& \frac{2}{1} \end{array}\end{align*}$
::优胜结果(对红)=21

You can solve any probability problem in terms of odds rather than probabilities. Notice that the ratio represents what is being compared. Be sure that your numbers match the comparison.
::您可以从概率而不是概率的角度解决任何概率问题。请注意, 比率代表了正在比较的数值。请确定您的数值与比较相符。

You can use odds to calculate how likely an event is to happen. You can compare the odds in favor of an event with the probability that the event will actually occur.
::您可以使用概率来计算事件发生的可能性。您可以比较事件发生的概率和事件实际发生的概率。

Let’s look at an example.
::让我们举个例子。

Suppose the weather forecast states:
::假设天气预报说:

Odds in favor of rain: 7 to 3
::胜于雨水的奇数:7比3

These odds tell you not only the odds of rain, but also the odds of not raining.
::这些概率不仅能告诉你下雨的几率, 还能告诉你没有下雨的几率。

If the odds in favor or rain are 7 to 3, then the odds against rain are:
::如果胜算或胜算是7比3的话逆差是:

Odds against rain: 3 to 7
::降雨险数:3至7

Another way of saying that is:
::另一种说法是:

Odds that it will NOT rain: 3 to 7
::3到7天 3到7天

You can use this idea in many different situations. If you know the odds that something will happen, then you also know the odds that it will not happen.
::你可以在很多不同的情况下使用这个想法。如果你知道事情会发生的可能性,那么你也可以知道它不会发生的可能性。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Jamie’s rainy beach day.
::更早之前,

Jamie is trying to determine if he should go to the beach with his friends and is listening to the weather forecast.
::Jamie正试图确定他是否应该和朋友去海滩并且正在听天气预报

First, what is the ratio from the question?
::首先,问题的比例是多少?

Forecast: 4 in 5 chance of showers.
::预测:五分之四的淋浴机会。

Therefore it will rain 4 times out of 5.
::因此,五分之四下雨

The chances of it not raining are 1 in 5.
::不下雨的机会是五分之一

Next, write the ratio of favorable to total outcomes.
::接下来,写出对总结果有利的比例。

$\begin{aligned} \begin{array}{rcl} P (raining) & = & \frac{# of favorable outcomes}{total # of outcomes} \\ P (raining) & = & \frac{4}{5} \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} P \text{(raining)} &=& \frac{ \# \ \text{of favorable outcomes}}{\text{total # of outcomes}} \\ P \text{(raining)} &=& \frac{4}{5} \end{array}\end{align*}$
::P(REAIN) ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++######+++++++####+++++++++++++45+45+++#############################++45

Then express this fraction as a percent.
::然后将这个分数表示为百分比。

$\begin{aligned} \begin{array}{rcl} \frac{4}{5} & = & \frac{x}{100} \\ 5 x & = & 4 \times 100 \\ 5 x & = & 400 \\ \frac{5 x}{5} & = & \frac{400}{5} \\ x & = & 80 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{4}{5} &=& \frac{x}{100} \\ 5x &=& 4 \times 100 \\ 5x &=& 400 \\ \frac{5x}{5} &=& \frac{400}{5} \\ x &=& 80 \end{array}\end{align*}$
::45=x1005x=4x1005x=4x1005x=4005x5=4005x=80

The answer is 80.
::答案是80

There is an 80% chance of rain.
::80%的雨是有可能下雨的。

Example 2
::例2

What are the odds in favor of a number cube landing on 4?
::数立方体在4点降落的几率有多大?

First, find the favorable and unfavorable outcomes.
::首先,找到有利和不利的结果。

Favorable outcomes = 1(4)
::有利结果=1(4)

Unfavorable outcomes = 5(1, 2, 3, 5, 6)
::不利结果=5(1,1、2,3,3,5,6)

Next, write the ratio of favorable to unfavorable outcomes.
::接下来,写下有利结果与不利结果的比例。

$\begin{aligned} \begin{array}{rcl} odds (4) & = & \frac{# of favorable outcomes}{# of unfavorable outcomes} \\ odds (4) & = & \frac{1}{5} \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \text{odds} \ (4) &=& \frac{ \# \ \text{of favorable outcomes}}{\# \ \text{of unfavorable outcomes}} \\ \text{odds} \ (4) &=& \frac{1}{5} \end{array}\end{align*}$
::不利结果(4)=15

The answer is $\begin{align*}\frac{1}{5}\end{align*}$ .
::答案是15岁

The odds in favor of rolling a 4 are 1 to 5.
::滚动4的赔率是1比5

Use this spinner to calculate odds.
::利用这个旋转器来计算几率。

Example 3
::例3

Calculate the odds in favor of spinning a blue.
::计算乘以旋转蓝色的概率

First, find the favorable and unfavorable outcomes.
::首先,找到有利和不利的结果。

Favorable outcomes = 1 (blue)
::有利结果=1(蓝色)

Unfavorable outcomes = 2 (red, yellow)
::不利结果=2(红色、黄色)

Next, write the ratio of favorable to unfavorable outcomes.
::接下来,写下有利结果与不利结果的比例。

$\begin{aligned} \begin{array}{rcl} odds (blue) & = & \frac{# of favorable outcomes}{# of unfavorable outcomes} \\ odds (blue) & = & \frac{1}{2} \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \text{odds} \ \text{(blue)} &=& \frac{ \# \ \text{of favorable outcomes}}{\# \ \text{of unfavorable outcomes}} \\ \text{odds} \ \text{(blue)} &=& \frac{1}{2} \end{array}\end{align*}$
::不利结果(蓝色) = 12

The answer is $\begin{align*} \frac{1}{2}\end{align*}$ .
::答案是12岁

The odds in spinning a blue are 1 to 2.
::旋转蓝色的几率是1比2

Example 4
::例4

Calculate the odds in favor of spinning a red or blue.
::计算乘以旋转红色或蓝色的概率。

First, find the favorable and unfavorable outcomes.
::首先,找到有利和不利的结果。

Favorable outcomes = 2 (blue or red)
::有利结果=2(蓝色或红色)

Unfavorable outcomes = 1 (yellow)
::不利结果=1(黄)

Next, write the ratio of favorable to unfavorable outcomes.
::接下来,写下有利结果与不利结果的比例。

$\begin{aligned} \begin{array}{rcl} odds (blue or red) & = & \frac{# of favorable outcomes}{# of unfavorable outcomes} \\ odds (blue or red) & = & \frac{2}{1} \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \text{odds} \ \text{(blue or red)} &=& \frac{ \# \ \text{of favorable outcomes}}{\# \ \text{of unfavorable outcomes}} \\ \text{odds} \ \text{(blue or red)} &=& \frac{2}{1} \end{array}\end{align*}$
::不利结果(蓝色或红色) = 21 的(蓝色或红色)不优惠结果 = ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++(蓝色或++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

The answer is $\begin{align*}\frac{2}{1}\end{align*}$ .
::答案是21岁

The odds in spinning a blue or a red are 2 to 1.
::旋转蓝色或红色的概率是 2比1。

Example 5
::例5

Calculate the odds against spinning a red or blue.
::计算在旋转一个红色或蓝色时的概率。

First, find the favorable and unfavorable outcomes.
::首先,找到有利和不利的结果。

Favorable outcomes = 2 (blue or red)
::有利结果=2(蓝色或红色)

Unfavorable outcomes = 1 (yellow)
::不利结果=1(黄)

Next, write the ratio of favorable to unfavorable outcomes.
::接下来,写下有利结果与不利结果的比例。

$\begin{aligned} \begin{array}{rcl} odds (against red or blue) & = & \frac{# of unfavorable outcomes}{# of favorable outcomes} \\ odds (against red or blue) & = & \frac{1}{2} \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \text{odds} \ \text{(against red or blue)} &=& \frac{ \# \ \text{of unfavorable outcomes}}{\# \ \text{of favorable outcomes}} \\ \text{odds} \ \text{(against red or blue)} &=& \frac{1}{2} \end{array}\end{align*}$
:红色或蓝色)+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

The answer is $\begin{align*}\frac{1}{2}\end{align*}$ .
::答案是12岁

The odds against spinning a blue or a red are 1 to 2.
::反对旋转蓝色或红色的概率是1比2。

Review
::回顾

1. For rolling a number cube, what are the odds in favor of rolling a 2?
::1. 如果滚动一个数字立方体,赞成滚动一个2的几率有多大?

2. For rolling a number cube, what are the odds against rolling a 2?
::2. 滚动一个数字立方体的概率有多大?

3. For rolling a number cube, what are the odds in favor of rolling a number greater than 3?
::3. 对于滚动数字立方体来说,滚动数大于3的几率有多大?

4. For rolling a number cube, what are the odds in favor rolling a number less than 5?
::4. 对于滚动一个数字立方体,赞成滚动数字小于5的几率有多大?

5. For rolling a number cube, what are the odds against rolling a number less than 5?
::5. 对于滚动一个数字立方体来说,如果滚动不到5个数字,其概率有多大?

6. For rolling a number cube, what are the odds in favor of rolling an even number?
::6. 对于滚动数字立方体来说,滚动偶数的几率有多大?

7. For rolling a number cube, what are the odds against rolling an even number?
::7. 对于滚动一个数字立方体来说,对偶数滚动的几率有多大?

For a spinner numbered 1 –10, answer the following questions.
::对于编号1 - 10的旋筒,请回答下列问题。

8. For spinning the spinner, what are the odds in favor of the arrow landing on 10?
::8. 对于旋转旋翼者来说,箭在10点钟降落的几率有多大?

9. For spinning the spinner, what are the odds in favor of the arrow landing on a 2 or 3?
::9. 对于旋转旋翼者来说,箭落到2或3时的几率有多大?

10. For spinning the spinner, what are the odds in favor of the arrow landing on 7, 8 or 9?
::10. 对于旋转旋翼者来说,箭落到7、8或9时的几率有多大?

11. For spinning the spinner, what are the odds in favor of NOT landing on an even number?
::11. 对于旋转旋翼者来说,不偶数着陆的几率有多大?

12. For spinning the spinner, what are the odds of the arrow NOT landing on 10?
::12. 对于旋转旋翼者来说,箭头不降落在10时的几率是多少?

13. For spinning the spinner, what are the odds in favor of the arrow landing on a number greater than 2?
::13. 对于旋转旋翼者来说,箭落到超过2码的箭头的几率有多大?

14. For spinning the spinner, what are the odds in favor of the arrow NOT landing on a number greater than 2?
::14. 对于旋转旋翼者来说,箭头不降落在大于2的号码上的可能性有多大?

15. For spinning the spinner, what are the odds of the arrow not landing on a number greater than 3?
::15. 对于旋转旋翼者来说,箭头落到不超过3个数的箭头的几率有多大?

Review (Answers)
::回顾(答复)

Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键。

Resources
::资源

Section outline

General

使用结果或概率计算奇数

Outcomes ::成果成果成果

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Use this spinner to calculate odds. ::利用这个旋转器来计算几率。

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Outcomes
::成果成果成果

Examples
::实例

Example 1
::例1

Example 2
::例2

Use this spinner to calculate odds.
::利用这个旋转器来计算几率。

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源