The probability that a certain kind of component will survive a given shock test is `3/4` . Find the probability that among 5 components tested (i) Exactly 2 will survive (ii) At most 3 will survive

Assume that the probability that a bomb dropped from an aeroplane will strike a certain target is 0.2. If 6 bombs are dropped find the probability that (i) exactly 2 will strike the target. (ii) at least 2 will strike the target.

The probabilities that three children can win a race are 1/3,1/4 and 1/5 . Find the probability that any one can win the race.

The probability that a student entering university will graduate is 0.4. Find the probability that out of 3 students of the university: (i) none will graduate, (ii) only one will graduate, (iii) all will graduate.

A coin is tossed 6 times. Find the probability of getting (i) exactly 4 heads (ii) at least 1 head (iii) at most 4 heads .

Find the probability of getting 5 at most 3 times in four throws of a dice.

The probability that a student will receive A, B, C or D grade or 0.40, 0.3, 0.1 and 0.10 respectively. Find the probability that a student will receive. i. B or C grade ii. at most C grade.

The probability that a certain person will buy a shirt is 0.2, the probability that he will buy a trouser is 0.3, and the probability that he will buy a shirt given that he buys a trouser is 0.4. Find the probability that he will buy both a shirt and a trouser. Find also the probability that he will but a trouser given that he buys a shirt.

A dice is rolled twice. Find the probability that (i) 5 will not come up either time. (ii) 5 will come up exactly one time.

Given the probability that A can solve a problem is 2/3 and the probability that B can solve the same problem is 3/5. Find the probability that none of the two will be able to solve the problem.

A lot contains 20 articles. The probability that the lot contains exactly 2 defective articles is 0.4 and the probability thatthe lot contains exactly 3 defective articles is 0.6. Articles are drawn in random one by one without replacement andtested till all the defective articles are found. What is the probability that the testing procedure ends at the twelfth testing ?