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

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 the conditional probability rule. Note that the ace has the highest value.

A= event a card higher than a 9 is selected

B= evenr a card between 7 and 10, inclusive is selected

C= an event a heart is selected

a. Find P(B).

b. Find P(B|A).

c. Find P(B|C).

d. Find P(B|(not A))

e. Find P(A).

f. Find P(A|B)

g. Find P(A|C).

Explanation / Answer

Solution:-

a) P(B) = 0.3077

B = event a card between 7 and 10, inclusive is selected

Number of cards in event B = 4 × 4 = 16

Total number of cards = 52

P(B) = 16/52 = 0.3077

b) P(B|A) = 0.20

A = event a card higher than a 9 is selected

N(A) = 20

N (B and A occurs) = 4

P(B|A) = 4/20 = 0.20

c) P(B|C) = 0.308

C = an event a heart is selected

N(C) = 13

N(B and C) = 4 (There are one 4 hearts between 7 and 10 )

P(B|C) = 4/13 = 0.308

d) P(B|(not A)) = 0.375

not A = Event  card smaller than a or equal to 9 is selected

N (not A) = 52 - 20 = 32

N(B and not A) = 12

P(B|(not A)) = 12/32 = 0.375

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