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 at least  one member is  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 ≥ 1) = 1 - P (X < 1) 

= 1 - P (X = 0)

`= 1 - "^4C_0   p^0  q^4`

`= 1 - 1 xx (0.3)^4`

= 1 - 0.0081

= 0.9919

Probability of at least one member is successfully treated is 0.9919.