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

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

Pratik Bendale · Accepted Answer

Final Answer : C, Explanation :  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 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

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