Let P(E1, E2) denote the event that exactly one out of E1 and E2 occurs. For three events A, B, C; it is known that P(A, B) = P(B, C) = P(C, A) = p and P(A∩B∩C)=p2 where 0 < p < 12. Then probability that at least one of A, B, C occur is

Let P(E1, E2) denote the event that exactly one out of E1 and E2 occur

1.	Let P(E1, E2) denote the event that exactly one out of E1 and E2 occurs. For three events A, B, C; it is known that P(A, B) = P(B, C) = P(C, A) = p and P(A∩B∩C)=p2 where 0 < p < 12. Then probability that at least one of A, B, C occur is
Answer» Let P( $E_{1}, E_{2}$ ) denote the event that exactly one out of $E_{1} a n d E_{2}$ occurs. For three events A, B, C; it is known that P(A, B) = P(B, C) = P(C, A) = p and $P (A \cap B \cap C) = p^{2}$ where 0 < p < $\frac{1}{2}$ . Then probability that at least one of A, B, C occur is