Question

In a cellular phone system, a mobile phone must be paged to receive a phone call. However, paging attempts don’t always succeed because the mobile phone may not receive the paging signal clearly. Consequently, the system will page a phone up to three times before giving up. If the results of all paging attempts are independent and a single paging attempt succeeds with probability 0.8, sketch a probability tree for this experiment and find the probability P[F] that the phone receives the paging signal clearly.

Answer 1

Answer:

The correct response will be "0.992". The further explanation to the following question is given below.

Explanation:

The probability that paging would be beneficial becomes 0.8  

Effective paging at the very first attempted is 0.8

On the second attempt the success probability will be:

⇒  $0.2\times 0.8$

⇒  $0.16$

On the third attempt the success probability will be:

⇒  $0.2\times 0.2\times 0.8$

⇒  $0.032$

So that the success probability will be:

⇒  $0.8 + 0.16 + 0.032$

⇒  $0.992$