HELP HAVE HARD TIME SOLVING THIS PROBLEM THE ANSWER IS 056

HELP ! HAVE HARD TIME SOLVING THIS PROBLEM --- THE ANSWER IS   0.567

NEED TO SEE STEPS TO UNDERSTAND. THANK YOU

Solution

Here,

P(x<1|I) = 1 - exp(-1/2) = 0.39346934

P(x<1|II) = (1-0)/(5-0) = 0.2

Thus,

P(I|x<1) = P(I) P(x<1|I) / P(x<1)

As

P(x<1) = P(I) P(x<1|I) + P(II) P(x<1|II) = 0.40*0.39346934 + 0.60*0.2 = 0.277387736

Thus,

P(I|x<1) = 0.40*0.39346934/0.277387736 = 0.567392554 [ANSWER]