Whenever horses a,b,c race together, their respective probabilities of winning the race are `0.3,0.5, and 0.2,` respectively. If they race three times, the probability that the same horse wins all the three races, and the probability that a,b,c each wins one race are, respectively

A die is thrown three times, find the probability that 4 appears on the third toss if it is given that 6 and 5 appear respectively on first two tosses.

The probabilities for A, B, and C hitting a target are (1)/(3), (1)/(5) and (1)/(4) respectively. If they try together, find the probability of exactly one shot hitting the target.

If the probability of winning a game is 0.3, what is the probability of loosing it ?

Three critics review a book. Odds in favour of the book are 5:2, 4:3 and 3:4 respectively for three critics. Find the probability that the majority are in favour of the book.

A machine operates only when all of its three components function. The probabilities of the failures of the first, second and third components are 0.14, 0.10 and 0.05 respectively. What is the probability that the machine will fail.

A problem on mathematics is given to three students A, B, C whose probabilities of solving it are (1)/(3), (2)/(5) and (3)/(4) respectively. Find the probability that the problem is solved.

A is targeting to B, B and C are targeting to A. Probability of hitting the target by A, B and C are (2)/(3), (1)/(2) and 1/3, respectively. If A is hit, then find the probability that B hits the target and C does not.

Two sets of candidates are competing for the position on the board of directors of a company. The probabilities that the first and second sets will win are 0.6 and 0.4 respectively. If the first set wins, the probability of introducing a new product is 0.8 and the corresponding probability if the second set wins is 0.3. What is the probability that the new product will be introduced ?

Two events A and B have probabilities 0.25 and 0.50 respectively the probability that both A and B occur simultaneously is 0.14 find the probability that neither A nor B occurs.

The probabilities of solving a problem by three students A,B,C are 3/7,3/8,and 1/3 if all of them try independently find the probability that the problem is not solved.