Question

Probabilities of A and B solving a specific problem are 2/3 and 3/5, respectively. If both of them try independently to solve the problem, then find the probability that the problem is solved.

In a game of Archery, each ring of the Archery target is valued. The centremost ring is worth 10 points and rest of the rings are allotted points 9 to 1 in sequential order moving outwards. Archer A is likely to earn 10 points with a probability of 0·8 and Archer B is likely the earn 10 points with a probability of 0·9. Based on the above information, answer the following questions : If both of them hit the Archery target, then find the probability that

Events A and B are such that P(A) = 1/2, P(B) = 7/12 and P(A̅ ∪ B̅) = 1/4. Find whether the events A and B are independent or not.

Events A and B are such that P(A)=1/2, P(B) = 7/12 and P(A̅∪B̅) = 1/4 Find whether the events A and B are independent or not.