Question

Two cards are chosen from those shown below, without replacement (13 cards are shown). What is the probability that both cards are multiples of 3? Express your answer as a decimal and round to the nearest thousandths.

Answer 1

`(1)/(26)`

Explanation:

n(S₁) = 13

A = {1st card is multiples of 3} (card no.3, 6, and 9)

n(A) = 3

P(A) =
`(3)/(13)`

B = {2nd card is multiples of 3}

n(B) = 2 (1 card of multiple 3 already withdrawn)

n(S₂) = 12 (1 card already withdrawn)

P(B) =
`(2)/(12)`

=
`(1)/(6)`

P(A∩B) =
`(3)/(13) *(1)/(6)`

=
`(1)/(26)`