You are dealt a hand of three cards,one at a time.Find the probability that your third card is your first ace.
A)0.077
B)0.00018
C)0.068
D)0.145
E)0.127

Question

Quizplus · Accepted Answer

There are 4 aces in a deck of 52 cards. So when you draw the first card, the probability of getting an ace is 4/52.

Now suppose you did not get an ace on the first card. This leaves 51 cards and 3 aces in the deck. So the probability of getting an ace on the second card, given that you did not get an ace on the first card, is 3/51.

Finally, suppose you did not get an ace on the first two cards. This leaves 50 cards and 2 aces in the deck. So the probability of getting an ace on the third card, given that you did not get an ace on the first two cards, is 2/50.

Therefore, the probability that your third card is your first ace is given by:

(4/52) x (3/51) x (2/50) = 0.068, which is closest to answer choice C.

You Are Dealt a Hand of Three Cards,one at a Time.Find