Three cards are dealt from a shuffled standard deck of playing cards. What is th

Question

Three cards are dealt from a shuffled standard deck of playing cards. What is the probability that the three cards dealt are, in order, an ace, a face card, and a 9? (A face card is a jack, queen, or king.) Let the events be defined as follows. A = an ace is dealt B = {a face card is dealt} C = {a 90 is dealt} We want to find the probability of the event A followed by B followed by C". To do this we first need to will find P(A), the probability that an ace is dealt first. Then we will need to find the conditional probability that B, a face card is dealt, will occur given that A, an ace is dealt, has already occurred. Finally, we will need to find the conditional probability that c, a 9 is dealt, will occur given that A and B have already occurred. Once these three probabilities are found we can use the equation below to find the solution. P(A followed by B followed by C) = P(B/A) middot P(C/A and B) We will first find P(A), the probability an ace is dealt. When choosing the first card, there are aces in a deck of 52 cards, so P(A) =. Now we will need to find the conditional probability that B, a face card is dealt, will occur given that A, an ace is dealt, has already occurred. Since we must assume that an ace has already been dealt, there 1 less card in the deck. Therefore, the second card is picked from the remaining cards. Of the cards remaining in the deck, there are face cards. Therefore, P(BA) = .

Explanation / Answer

Solution :

When the first card is an ace then we have 51 cards remaining in the deck and one card is to be picked now.

The remaining number of face cards are 12 ( 3 from each suit ) as the first one was an ace .

Therefore the probability that we will get an ace now is P( B|A ) = 12/51

= 4/17

Answer

TY!

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