PS - Probability

[ruwan_s]

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

ANS: D



Would like some advice on how to set up the question. I understand that only 5 numbers out of 6 are involved in contributing to a sum of 8.

[GMATGuruNY]

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

Ways to get a sum of 8:
2, 6
3, 5
4, 4
5, 3
6, 2

As the options in red indicate, 2 of the 5 ways include a card numbered 5.
Thus:
P(a card numbered 5 is drawn) = 2/5.

The correct answer is D.

[ruwan_s]

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

Way to get a sum of 8:
2, 6
3, 5
4, 4
5, 3
6, 2

As the options in red indicate, 2 of the 5 ways include a card numbered 5.
Thus:
P(a card numbered 5 is drawn) = 2/5.

The correct answer is D.

Thank you Mitch, you made it look so easy!