Question

Is a and b are independent events p(a)=y and p(b)=2y and p(exactly one of a,b)=5/9 then find y?

Answer 1

The possible values of y are 1/3 and 5/12.

• Since a and b are independent events, the probability of both a and b occurring simultaneously is equal to p(a).p(b)=2y².
• The probability of exactly one of a and b occuring is equal to the sum of individual probabilities of a and b minus twice the probability of a and b occurring simultaneously.
• So, y+2y-4y²=5/9.
• Solving the above quadriatic equation we get the desired values of y.