Question

A mattress store sells only king, queen and twin-size mattresses. Sales records

at the store indicate that one-fourth as many queen-size mattresses are sold

as 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.

Answer 1

Let k be the relative frequency of selling king size mattresses
Let q be the relative frequency of selling queen size mattresses
Let t be the relative frequency of selling twin size mattresses

we are given

k = 3t

Using the two equations we get

We know that the total probability

k+q+t = 1
3t + t + t = 1
t=1/5

Hence q = 1/5
k = 3/5

the probability that the next mattress sold is either king or queen- size= 1/5 + 3/5 = 4/5 = 0.8