An employer wishes to hire three people from a group of 15 applicants 8 men and 7 women, all of which are equally qualified to fill the position . if the three are selected at a random. what is the probability, a) All will be men? b) at least one will be a women?
To find the probability of each scenario, we need to use the concept of combinations and apply the formula for probability.
a) Probability that all three will be men:
First, we need to determine the total number of ways to select three people out of fifteen. This can be calculated using combinations.
Number of ways to select 3 people out of 15 = 15C3 = (15!)/(3!(15-3)!) = 455
Next, we need to determine the number of ways to select three men out of the eight available men.
Number of ways to select 3 men out of 8 = 8C3 = (8!)/(3!(8-3)!) = 56
Therefore,
Probability (all three will be men) = Number of ways to select 3 men out of 8 / Number of ways to select 3 people out of 15
= 56/455
= 0.1231 (rounded to four decimal places)
So, the probability that all three will be men is approximately 0.1231.
b) Probability of at least one woman being selected:
To find the probability of at least one woman being selected, we can find the probability of the complementary event, i.e., no women being selected, and then subtract it from 1.
Number of ways to select 3 men out of 15 (including no women) = 8C3 = 56
Therefore,
Probability (no women being selected) = Number of ways to select 3 men out of 8 / Number of ways to select 3 people out of 15
= 56/455
= 0.1231 (rounded to four decimal places)
Since no women are selected in this case, the probability of at least one woman being selected is:
Probability (at least one woman being selected) = 1 - Probability (no women being selected)
= 1 - 0.1231
= 0.8769 (rounded to four decimal places)
So, the probability of at least one woman being selected is approximately 0.8769.
Done yesterday for you
http://www.jiskha.com/display.cgi?id=1446710013
Always check back in your previous post before reposting the same question.
I just noticed that you changed the last part of the question.
In this new version simply take
1 - (answer to a) )
(if we exclude the "all men" case there must be at least one woman in the group)