Question

A new treatment for baldness is known to be effective in 70% of the cases treated. Four bald members from different families are treated. Find the probability that exactly two members are successfully treated.

Answer 1

Let X : be the number of members successfully treated out of 4 members. 

∴ X = 0,1,2,3,4

n = 4

p = `70/100 = 0.7`

q = 1 - 0.7 = 0.3

∴ The binomial distribution is 

X ~ B (4 , 0.7) and pmf is

p (X = x ) = `"^4C_x   p^x   q^(4 -x)`

 

P (X = 2) = `"^4C_2  (0.7)^2 . (0.3)^2`

`= 6 xx 0.49 xx 0.09`

= 0.2646

Probability of exactly two members successfully treated 0.2646.