IIM Bangalore (UGAT) Modern Math > Probability PYQs

A sportsperson could be an expert in badminton and / or squash. Given that someone is a squash expert, the probability that they are expert at badminton as well is 0.8. There are twice as many badminton experts as there are squash experts. Given that Saina is a badminton expert, what is the likelihood that she is an expert in squash?

Let A, B, and C be the three mutually independent events with their probabilities equal to $x, y$ and $z$ respectively. Then the probability that exactly two of these events occur is

A ten-digit number is selected at random from the set of all possible ten-digit numbers. The probability that the sum of the ten digits in this selected number is odd, is nearest to