Job Applications Six men and seven women apply for two identical jobs. If the jobs are filled at random, find the following:
$$
\begin{array}{l}{\text { a. The probability that both are filled by men. }} \\ {\text { b. The probability that both are filled by women. }} \\ {\text { c. The probability that one man and one woman are }} \\ {\text { hired. }} \\ {\text { d. The probability that the one man and one woman }} \\ {\text { who are twins are hired. }}\end{array}
$$

Answer

a. 0.192 b. 0.269 c. 0.538 d. 0.013

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Intro Stats / AP Statistics

Elementary Statistics a Step by Step Approach

Chapter 4

Probability and Counting Rules

Section 5

Probability and Counting Rules

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Video Transcript

Okay, so in this question, it is given. There are six six man on board, seven women. Ah, playing for two identical jobs. Now the jobs are it is given this filled by random onboard. The first question you are asking us What is the property that both are filled by Mac? That means probably off getting water, man. So we know probability means it is basically number off favorable cases by total number of cases. So first we signed find equities. Total number of is here. That means here we're going to select two people out off 13 people. So total number of ways will be 13th seed to. So when we're taking the first case Author of men. So six months. Other six, man is there out of that? We're going to take two people on Tory. Number of case. We know 13 seats. This will be the required probability number of favorable case by the total number of cases. So 62 we find six, it will become 15 13 state to we found out we get 78 15 5 78. We can write a 0.19 to this will be required. Us Now, in the second part of this question, it is asking, What is the probability that both are human? No border of women means again. Total number of case you're selecting two people will be 13 C two, so the denominator don't change now in the numerator. What happens is we have to select two women out of seven that you can do. But if you think 72 ways, 72 by 13 seats will come 72. When you find out we'll be getting 21 13 seat will be 78 so it's racially can express has 0.269 This will be the answer for second question. Now, in the third question is given property that oneness, man on oneness. Everyone, one man and one woman. How we can select one man were selected Means we can see there are six months or six men that you can select by 61 7 women. You can select one by using 71 ways out of 60 per year, selecting one out of seven papers, selective one like that, divided by total, your selecting two people out off 13 so they didn't see it would come So this is basically 16 to 7, but 78 we get 42 by 78 that we can express this point 538 That will be the answer for the third question. No. In the last question it is given, we have to find the probability that one man and one woman are selected aunt. They are tweets. So two people getting center districts. So, you know, Twins year selected mix. You know, suppose there is a one twin seven. So we had to select both south off to people how to select all these two people. That means that you can do by using to see two ways. Okay, out off. Do we have to select two? They were by out off 13. You have to select toe. That will be the total cases. Okay, So favorable cases to see to total cases. 13 ft. So this one you can write us to see two is equal to one 13 ft. Toby already found out 78 so answer will be won by 78 that you can express like 0.13 So these are required probabilities

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