Question

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

A box B₁ contains 1 white ball and 3 red balls. Another box B₂ contains 2 white balls and 3 red balls. If one ball is drawn at random from each of the boxes B₁ and B₂, then find the probability that the two balls drawn are of the same colour.

A bag contains cards numbered 1 to 25. Two cards are drawn at random, one after the other, without replacement. Find the probability that the number on each card is a multiple of 7.

Rohit, Jaspreet and Alia appeared for an interview for three vacancies in the same post. The probability of Rohit's selection is 1/5, Jaspreet's selection is 1/3 and Alia's selection is 1/4. The event of selection is independent of each other.