Mr. X. Marketing director for ABC film production believes that the studio upcoming firm has a 70% chance of being hit, a 20% chance of being moderate and 10% chance of being a flop. To test his opinion Mr. .X organized two screenings. After each screening, the audience rates the film on a scale of 1 and 5 stars. From the past long experience it is known that a hit film will receive 4 or 5 stars 65% of the time,30% of the time it will receives 2 or 3 stars and 5% of the time it will receive ratings of 1 star. For the moderately successful film, the respective probabilities are 0.30,0.50 and 0.20 for flop. The respective probabilities are 0.10, 0.40 and 0.50 the results of two screening tests are independent of each other. Required :
a) If the first screening produces a score of 3 stars, what is the probability that a film is hit?
b) If the screening test produces a score of 3 stars and the second screening results in a score of 1 stars, what is the probability that a film is flop?.