Answer to Question #125373 in Statistics and Probability for rohi

Question

A survey of two new antidandruff shampoos A and B was conducted by a healthcare organization. 3/4 of the people who bought shampoo A got rid of dandruff, whereas the 7/8 of the people who used shampoo B were satisfied with the shampoo. Among the surveyed people, 3/4 of them bought shampoo A while the rest bought shampoo B. What is the probability of people getting rid of dandruff irrespective of which shampoo they used?

Answer 1

Solution:

A $\bigcup$ B=U

A $\bigcap$ B=$\varnothing$

"3/4 of them bought shampoo A", so P(A)=3/4,

"the rest bought shampoo B", so P(B)=1-3/4=1/4.

Let P(C) - the probability of people getting rid of dandruff.

"3/4 of the people who bought shampoo A got rid of dandruff", so P(C|A)=3/4,

"the 7/8 of the people who used shampoo B were satisfied with the shampoo", so P(C|B)=7/8.

Then

P(C)=P(C|A)P(A)+P(C|B)P(B)

P(C)=3/4*3/4+7/8*1/4

P(C)=25/32.

Answer:

The probability of people getting rid of dandruff is equel 25/32.