Let A and B be two events representing two disasters car acc

Let A and B be two events representing two disasters (car accident and broken arm) for which P(A) = .01, P(B) = .02, and P(A B) = .004. (a) What is P(A B)? (b) What is the meaning of P(A\\B) and P(B\\A) ? Calculate both probabilities. (c) Are A and B independent? Does your answer make sense?

Solution

A) P(A U B) =P(A)+P(B)-P(A intersection B )

= 0.01+0.02-0.004

=.026

B) P(A/B) is the probability of occurance of A but but not B

And P(B/A) is the probability of occurance of B but not A.

P(A intersection B )= P(A).P(B/A)

P(B/A)=.004/.01=.4

P(A intersection B )= P(B).P(A/B)

P(A/B)= .004/.02=0.2

C) P(A intersection B) =.004 not equal to P(A).P(B)=.002