A card is selected from a deck of 52 playing cards. Find the probability of selecting

Question

· a prime number under 10 given the card is a heart. (1 is not prime.)
· a diamond or heart given the card is red.
· a King, given that the card is not a spade.

Show step by step work. Give all solutions exactly in reduced fraction form

Answer 1

conditional probability:
P(A|B) read: prob of A, given B
= P(A∩B)/P(B)

let A be all primes under 10
B is all hearts
so A∩B is 2H, 2H, 5H, 7H, there are 4 of those

prob(prime under 10 | red) = (4/52)/(1/4) = 4/13

Here is a page with a nice explanation and examples of conditional probability.

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