Problem Solving

Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is numbered 5 ?

A. 1/6
B. 1/5
C. 1/3
D. 2/5
E. 2/3

Please explain. Thanks.

If the sum of the numbers is 8 and one of the cards is 5, then there are five possibilities - 2&6, 3&5, 4&4, 5&3 and 6&2.

Thus there are 2 ways that the sum can be 8 when one card is 5.

So probability is 2/5. Answer is D.

Thanks. Makes sense.