A new surgical procedure is successful with a probability of p. Assume that the operation is performed five times and the results are independent of one another. What is the probability that

a all five operations are successful if p = .8?

b exactly four are successful if p = .6?

c less than two are successful if p = .3?

Step 1 of 3</p>

a) We have to find the probability of all operations are successful if p=0.8

And q=1-0.8

=0.2

Given that the operation is performed 5 times

Then n=5

Let X be the no.of successful operations

Then

The pmf of binomial distribution is

P(all operations are successful)=P(X=5)

=0.32768

Hence the probability of all operations are successful is 0.32768

Step 2 of 3</p>

b) We have to find the probability of exactly 4 operations are successful if p=0.6

And q=1-0.6

=0.4

Here

P(Exactly 4 are successful)=P(X=4)

=

=0.2592

Hence the probability of exactly 4 operations are successful is 0.2592