The probability that a particular day in the month of July is a rainy day is `3/4` . Two person whose credibility are `4/5` and `2/3` , respectively, claim that 15th July was a rainy day. Find the probability that it was really a rainy day.

The probability that a man buying a shirt is 0.2 and that for buying a trouser is 0.3. The probability that he will buy a shirt given that he buys a trouser is 0.4. i. Find the probability that he will buy both a shirt and a trouser ii. Find the probability that he will buy a trouser, given that he buys a shirt.

Find the probability that the birth days of six different persons will fall in exactly two calendar months.

Three persons work independently on a problem. If the respective probabilities that they will solve it are 1/3, 1/4 and 1/5, then find the probability that not can solve 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 eh majority are in favour of the book.

The probability that a certain kind of component will survive a electrical test is (3)/(4) . Find the probability that exactly 3 of the 5 components tested survive .

Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3 respectively. They are rolled and the sum of the numbers on them is noted. Find the probability of gettting each sum from 2 to 9 separately.