Question

If two people are randomly chosen from a group of eight women and six men, what is the probability that (a) both are women; (b) both are men; (c) one is a man and the other a woman?

Answer 1

(A. both men and women) i had to get it qrong on my test to find the right answer...you are welcome

Answer 2

a) Choice 1: 8 women out of 14 total, Choice 2: 7 women out of 13 remaining

`(8)/(14)` x
`(7)/(13)` =
`(8(7))/(14(13))` =
`(8)/(26)` ≈ 30.8%

b) Choice 1: 6 men out of 14 total, Choice 2: 5 men out of 13 remaining

`(6)/(14)` x
`(5)/(13)` =
`(6(5))/(14(13))` =
`(15)/(91)` ≈ 16.5%

c) Choice 1: 8 women out of 14 total, Choice 2: 6 men out of 13 remaining

`(8)/(14)` x
`(6)/(13)` =
`(8(6))/(14(13))` =
`(24)/(91)` ≈ 26.4%