Two cards are selected in sequence from a standard 52-card deck. Find the probab

Question

Two cards are selected in sequence from a standard 52-card deck. Find the probability that the second card is a six, given that the first card is a diamond. One satellite is scheduled to be launched from Cape Canaveral in Florida, and another launching is scheduled for Vandenberg Air Force Base in California. Let A denote the event the Vandenberg launch goes off on schedule, and let B represent the event that the Cape Canaveral launch goes off schedule. If A and B are independent events with P(a) > P(B), P(A B) = 0.626, and P(A B) = 0.144, determine the values of P(A) and P(B) to three decimal places.

Explanation / Answer

18.

Let

6D = the first card is a 6 of diamonds
xD = the first card is a diamond that is not a 6
D = the first card is a diamond
6 = second card is a 6

Thus,

P(6|D) = P(6D|D)*P(6|6D) + P(xD|D)*P(6|xD)

= (1/13)*(3/51) + (12/13)*(4/51)

= 0.076923077 [ANSWER]

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