Question

QN. A company produces 2 types of clothes,T shirts and trousers.if one buy purchasing T shirt ,there is 90% chances of purchasing T shirt next.If one purchase Trouser ,there is 80% chances of purchase  trouser next.

a)If a person is a Trouser purchaser ,what is the probability of purchasing T shirt two purchases from now?

b)If a person is a T shirt purchaser ,what is the probability of purchasing T shirt three purchases from now?

Answer 1

a) Suppose he purchased trouser. Next he may purchase t-shirt with probability , and purchase trouser with probability .

If he purchases t-shirt, the probability of his purchasing t-shirt next is . Thus, the probability that he purchases trouser, then t-shirt and then t-shirt is .

If he purchases trouser, the probability of his purchasing t-shirt next is . Thus, the probability that he purchases trouser, then trouser and then t-shirt is .

Hence, the probability that he purchases t-shirts two steps from now is .

b) Suppose he purchased t-shirt

His next three purchases can be one of the following, and no other:

Here, denotes that he purchased t-shirt, and denotes that he purchased trouser.

The probabilities associated to these triples are as follows:

Therefore, the probability that he purchases a t-shirt three steps from now is ​​​​​​​.