Wednesday, July 28, 2010

Conditional probability statistics problem, please advise?

Given that the first card is red, what鈥檚 the probability that the second card is an Ace? (no replacement). Hint: use the general multiplication rule.Conditional probability statistics problem, please advise?
Let A = Ace and B = Red





P(A|B) = P(A and B)/P(B)





P(B) = 26/52





P(A and B) is either





Pick red ace first and not pick red ace, but pick other ace second time





(1/52)(3/51) = 3/(52*51) OR





Pick red, but not ace of red first and pick ace second





(25/52)(4/51) = 100/(52*51)








P(A and B)/P(B) = [3/(52*51) + 100/(52*51)]/(26/52)





[103/(52*51)]*[52/26] = 103/(51*26) = 103/1326 = 0.0776772247

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