Question

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 _

Answer 1

(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