1. Given that P(B) = _ , P(C) = 4 , P(A |B) = = 1, P(CUB) = = , P(B| A) = Find: (a) P(BAC) (b) P(AMB) (c) P(A) (d) P(AVB) (e ) P(A B ) 2. For events A and B it is known that P(A) = 2, P(AUB)= and P(AMB) = 12 , Find P(B). 3. Of the married couples in a certain country, 60% of the husbands and 30% of the wives have full time jobs. For 10% of the couples, both have full time jobs. Draw a Venn diagram to show the events described above. Label your Venn diagram clearly. (b) Find the proportion of couples in which at least one member has a full time job. (c) Find the proportion of couples in which neither has a full time job. 4. I wo events are such that P(A) = 0.8, P(A/ B) = 0.5, P(A | B) =0.8. Calculate the probability that (a) B occurs, (b) B occurs given that A has occurred (c) At least one of the two events occurs 5. In a survey carried out for ASTRO, the viewing choices of 100 families were recorded. 46 families said they like to watch Channel 80 62 families said they like to watch Channel 63 13 families said they had not watched either channel. (i) Draw a complete Venn diagram for the given information above. By using the Venn diagram, or otherwise, calculate (1i) the probability of families who like to watch both channels. the probability of families who like to watch channel 80 only. (iv) the probability of families who like to watch channel 63 or channel 80 or both