Probability Tes...

A medicine is known to be 75% effective to cure a patient. If the medicine is given to 5 patients, what is the probability that at least one patient is curved by this medicine?

A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the arts becomes defective. What is the probability that the machine will not stop working?

There is $$25$$% chance that it rains on any particular day. What is the probability that there is at least one rainy day within a period of $$7$$ days?

Three independent events, $$A_1, A_2$$ and $$A_3$$ occur with probabilities $$P(A_i) = \dfrac{1}{1 + i}, i = 1, 2, 3$$. What is the probability that at least one of the three events occurs?

In a series of 3 one-day cricket matches between teams A and B of a college, the probability of team A winning or drawing are 1/3 and 1/6 respectively. If a win, loss or draw gives 2, 0 and 1 point respectively, then what is the probability that team A will score 5 points in the series?

A salesman has a $$70\%$$ chance to sell a product to any customer. The behaviour of successive customers is independent. If two customers A and B enter, what is the probability that the salesman will sell the product to customer A or B?

For two events, A and B, it is given that $$P(A) = \dfrac{3}{5}, P(B) = \dfrac{3}{10} $$ and $$P(A|B) = \dfrac{2}{3}$$. If $$\overline A$$ and $$\overline B$$ are the complementary events of A and B, then what is $$P(\overline A | \overline B)$$ equal to?

Three candidates solve a question. Odds in favour of the correct answer are $$5 : 2, 4 : 3$$ and $$3 : 4$$ respectively for the three candidates. What is the probability that at least two of them solve the question correctly?

A student appears for tests I, II and III. The student is considered successful if he passes in tests I, II or I, III or all the three. The probabilities of the student passing in tests I, II and III are m, n and $$\dfrac{1}{2}$$ respectively. If the probability of the student to be successful is $$\dfrac{1}{2}$$, then which one of the following is correct?

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probabilities of an accident involving a scooter driver, car driver and a truck driver are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. The probability that the person is a scooter driver is