Question

The probability that a patient recovers from a ceartin type of operation is 0.78

(a) What is the probability that 3 of the next 4 patients who have this operation survive?

(b) What is the probability that all of the next 4 patients who have this operation survive?

(a) The probability is ______

Answer 1

Let , X be the number of patients who have this operation survive.

p = probability that a patient recovers from a certain type of operation = 0.78

n = 4

X follows Binomial distribution with p = 0.78 and n = 4

a )

We have to find probability that 3 of the next 4 patients who have this operation survive.

i. e. P( x = 3 )

Using Excel function ,   =BINOMDIST( x, n, p, 0)

P( x = 3 ) = BINOMDIST( 3 , 4 , 0.78, 0 ) = 0.4176

Probability that 3 of the next 4 patients who have this operation survive 0.4176

b)

We have to find probability that all of the next 4 patients who have this operation survive.

i.e P( x = 4 )

Using Excel function ,   =BINOMDIST( x, n, p, 0)

P( x = 4 ) = BINOMDIST(4 , 4 , 0.78, 0 ) = 0.3702

Probability that all of the next 4 patients who have this operation survive is 0.3702