Question

I have a couple math questions.

#1 The probability of randomly selecting a 4 person committee consisting entirely of women from a pool of 15 men and 17 women is ___

#2 Getting a sum of either 4,5, or 9 on a roll of two dice. Is it overlapping or non-overlapping and what is the probability of the combined event?

#3 You draw one card from a 52 card deck. Then the card is replaced in the deck and the deck is shuffled, and you draw again. Find the probability of drawing a diamond each time.

Answer 1

1)total person=15+17=32

The probability of randomly selecting a 4 person committee consisting entirely of women from a pool of 15 men and 17 women

= 17C4 / 32C4 =2380/35960=0.0662

2)

favorable cases of sum of 4(1,3)(3,1)(2,2) = 3

sum of 5

(1,4)(4,1)(2,3)(3,2)=4

sum of 9

(3,6)(6,3)(4,5)(5,4) = 4

it is non-overlapping (no outcome of sum of 4,5and 9 overlapped)

probability of the combined event = (4+4+3)/36 = 11/36

3)

total diamond cards =13

P(both cards diamond) = P(diamond in first draw)*P(diamond in second draw) = 13/52*13/52=1/16