Thank you 4 Let A1 and A2 be events such that PA1 06 PA2 0

Thank you!

4. Let A1 and A2 be events such that P[A1] = 0.6, P[A2] = 0.4. and P[A1 UA2] = 0.8. Are A1 and A2 independent? .Justify your answer.

Solution

Two events are dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed.

Over here, P(A) happening and the P(A | B) i.e probability of A occuring given that B has already occured are not the same.

P(A) = 0.6

P(B) = 0.4

P(A U B ) 0.8

So, P ( A and B ) = 0.6 + 0.4 - 0.8

= 0.2

Thus,

P(A) = 0.6

P(A | B) = 0.2 / 0.4 = 0.5

Thus, the two evets are dependent.

Hope this helps.Ask if you have doubts.