8.3  Probability · Part 7

drawing a black ball in the first attempt is P ( A ) = Probability of drawing the second black ball given that the first ball drawn is black P(B/A) = ∴ The probability that both balls drawn are black is given by P(A ∩ B) = P(A) P(B/A) = × Example . In a shooting test the probability of hitting the target are for A , for B and for C . If all of them fire at the same target, calculate the probabilities that (i) All the three hit the target (ii) Only one of them hits the target (iii) At least one of them hits the target Given P (A) = , P (B) = , P (C) = Then P A ( ) = − ; P B ( ) = − and P C ( ) = − (i) P( A )=(all the three hit the targets) = P(A ∩ B ∩ C)=P(A)P(B)P(C) (since A,B,C hits independently) = (ii) P (only one of them hits the target) = P ∩ ∩ ∪ ∩ ∩ ∪ ∩ ∩ ) ( ) ( { } = P P A     ) + (