Question

A card is drawn at random from a full pack of playing cards. It is not put back. A second card is then drawn from the same pack.

(a) Find the probability that:

(i) both cards are sevens

(ii) neither card is a seven

(iii) at least one seven is obtained

Answer 1

Since there are 4 sevens,
P(7) = 4/52 = 1/13

(i) P(7,7) = 1/13 * 3/51
(ii) P(~7,~7) = 12/13 * 47/51
(iii) P(7,~7) + P(~7,7) + P(7,7)
= 1/13 * 48/51 + 12/13 * 4/51 + 1/13 * 3/51