A mattress store sells only king, queen and twin-size mattresses. Sales records at the store indicate that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. Records also indicate that three times as many king-size mattresses are sold as twin-size mattresses.

Calculate the probability that the next mattress sold is either king or queen-size

• 0.12
• 0.15
• 0.80
• 0.85
• 0.95

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: C

Letting t denote the relative frequency with which twin-sized mattresses are sold, we have that the relative frequency with which king-sized mattresses are sold is 3t and the relative frequency with which queen-sized mattresses are sold is (3t+t)/4, or t. Thus, t = 0.2 since t + 3t + t = 1. The probability we seek is 3t + t = 0.80.

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.