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 8 is selected

B= Event a jack is selected

C= Event a heart is selected

ALL RESULTS HAVE TO BE EXPRESSED IN WORDS ALONG WITH ANSWER IN FRACTION FORM

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)

h. Find P(A|(not B)

Explanation / Answer

a)P(B) =P(jack is selected) =4/52 =1/13 (as there are 4 jacks in 52 cardS)

b)P(B|A) =P(jack given a card higher than 8) =4/20=1/5 (as there are 20 cards higher than 8 considering ace as lowest rank)

c) P(B|C) =P(jack selecting given card is of heart1/13 (as there are 13 heart cards out of which one is jack)

d) P(B|not A) =P(jack given a card is not higher than 8) =0 (as card can nt be jack if card is lower than 8)

e) P(A) =P(card is higher than 8) =20/52=5/13

f) P(A|B) =P(card higher than 8 given Jack) =1 (as jack is always higher than 8)

g) P(A|C) =P(card is higher than 8 given a heart) =5/13

h) P(A|not B) =P(card is higher than 8 given not Jack) =16/48 =1/3 (as there are 16 card higher than 8out of 48 which are not jack)

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