Question

# One card is selected at random from an ordinary deck of 52 playing cards. Events A,...

One card is selected at random from an ordinary deck of 52 playing cards. Events A, B, and C are defined below. Find the probabilities for parts (a) through (h) below and express your results in words. Compute the conditional probabilities directly: do not use conditional probability rule. Note that the ace has the highest value.

A = event a face card is selected

B = event a jack is selected

C = event a spade is selected

a. Find P(B). Express your result in words. The probability that _ is selected is _

b. Find P(B|A). Express your result in words The probability that _selected, given that _ selected is _

c. Find P(B|C). Express your result in words. The probability that _selected, given that _selected is _

d. Find P(B|(not A)). Express your result in words. The probability that _ selected, given that _ selected is _

e. Find P(A). Express your result in words. The probability that _ is selected is _

(a)

P(B) = The probability that Jack is selected is 4/52 = 1/13 = 0.0769

(b)

P(B/A) = Probability that Jack selected, given that Face card selected is = P(AB)/P(A) = 4/12 =1/3 = 0.3333

(c)
P(B/C) = The probability that Jack selected given that Spade selected = P(BC)/P(C) = 1/13 = 0.0769

(d)

P(B/ not A) = The Probability that Jack selected, given that not face card selected = 0

because First Face card not selected. So, there is no Jack.

(e)

P(A) = The probability that Face Card selected = 12/52 = 3/13 = 0.2308

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