The probabilities that a student passes in Mathematics,Physics and Chemistry are m, p and c, respectively. Of these subjects, the student has a 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Which of the following relations are true?

Probability that Hameed passes in Mathematics is 2/3 and the probability that he passes in English is 4/9. If the probability of passing both courses is 1/4. What is the probability that Hameed will pass in at least one of these subjects?

In the final examinations for 9^(th) grade students of New York Public School, 4 students failed in Mathematics Sceince and History, 16 students failed in at least two of the above - mentioned subjects and 25 students failed in at least one of the above subject . How many students failed in exactly one of the mentioned subjects ?

The probability to pass in an examination of mathematics for three students are 1/4,1/5,1/6 . Find the probability that at least two students will pass in this examination.

A probability of student A passing an examination is 2/9 and of student B passing is 5/9. Assuming the two events: A passes, B passes as independent, find the probability of : (i) only A passing the examination (ii) only one of them passing the examination.

If two switches S_1a n dS_2 have respectively 90% and 80% chances of working. Find the probabilities that each of eth following circuits will work.

A player tosses a coin and score one point for every head and two points for every tail that turns up. He plays on until his score reaches or passes n. P_(n) denotes the probability of getting a score of exactly n. Which of the following is not true ?

In a college, 70% students pass in Physics, 75% pass in Mathematics and 10% students fail in both. One student is chosen at random. What is the probability that: He passes in Physics and Mathematics.

A rifleman is firing at a distance target and hence has only 10% chance of hitting it. Find the number of rounds; he must fire in order to have more than 50% chance of hitting it at least once.

In a college 30 % students fail in physics , 25 % fail in mathematics and 10 % fail in both subjects .One student is chosen at random . The probability that she fails in physics if she has failed in mathematics is

In a class of 125 students 70 passed in Mathematics, 55 in statistics, and 30 in both. Then find the probability that a student selected at random from the class has passed in only one subject.