Probability quiz

P(A/B) is equal to:

If A and B are independent events, then P(A and B) equals:

A die is thrown. The probability of getting an even number given that the number is greater than 3 is:

P(E/E) is equal to:

If E1, E2, E3 form a partition of the sample space, then P(E1) + P(E2) + P(E3) is:

A random variable X takes values 0 and 1 with equal probability. Its mean is:

If P

The sum of all probabilities in a probability distribution is:

Two cards are drawn without replacement from a pack of 52. The probability that both are kings is:

Two mutually exclusive events with non-zero probabilities are:

If P

A coin is tossed three times. Find the probability of exactly two heads given that the first toss is a head. (2 marks)

If A and B are independent, prove that A and not-B are also independent. (2 marks)

A box has 5 red and 3 blue pens. Two pens are drawn one after another without replacement. Find the probability that both are red. (2 marks)

State Bayes' theorem. (2 marks)

If P

A die is thrown twice. Find the probability that the sum is 8 given that the first throw is 3. (2 marks)

Can P(X = x) = (x + 1)/10 for x = 0, 1, 2, 3 be a probability distribution? Justify. (2 marks)

Explain the difference between independent events and mutually exclusive events. (2 marks)

A card is drawn from a pack. Are the events drawing a spade and drawing an ace independent? Justify. (2 marks)

Given P

An urn contains 10 black and 5 white balls. Two balls are drawn one after the other without replacement. Find the probability that both are black. (3 marks)

A and B are independent events with P

A die is thrown twice and X denotes the number of sixes. Find the probability distribution of X and its mean. (3 marks)

In a school, 60% of students live in the hostel and 40% are day scholars. 30% of hostellers and 20% of day scholars get grade A. A student chosen at random has grade A. Find the probability that the student is a hosteller. (3 marks)

Read the passage and answer the questions. An insurance company insured 2,000 scooter drivers, 4,000 car drivers and 6,000 truck drivers. The probabilities of an accident are 0.01, 0.03 and 0.15 respectively. One insured person meets with an accident. (i) Write the prior probabilities of each type of driver. (ii) Find the total probability of an accident. (iii) Find the probability that the person is a scooter driver. (5 marks)

Read the passage and answer the questions. In a quiz, a problem is given to two students who work independently. Their probabilities of solving it are 1/2 and 1/3. (i) Find the probability that neither solves it. (ii) Find the probability that the problem is solved. (iii) Find the probability that exactly one of them solves it. (5 marks)

Read the passage and answer the questions. A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. (i) Define the events involved. (ii) Find the total probability that he reports a six. (iii) Find the probability that it is actually a six. (5 marks)

Read the passage and answer the questions. A box of 10 bulbs contains 4 defective bulbs. A shopkeeper draws 2 bulbs at random without replacement. Let X be the number of defective bulbs drawn. (i) Find P(X = 0) and P(X = 1). (ii) Find P(X = 2) and verify the total is 1. (iii) Find the mean of X. (5 marks)

Read the passage and answer the questions. A coin is tossed three times. E is the event of a head on the third toss and F is the event of heads on the first two tosses. (i) Find P(E), P(F) and P(E and F). (ii) Find P(E/F). (iii) Are E and F independent? (5 marks)

A doctor travels by train, bus, scooter or other means with probabilities 3/10, 1/5, 1/10 and 2/5. The probabilities of his being late are 1/4, 1/3 and 1/12 by train, bus and scooter, and he is never late by other means. If he is late, find the probability that he came by train. Draw a tree diagram. (6 marks)

A coin is tossed three times. Find the probability distribution of the number of heads, draw its bar diagram and find the mean. (6 marks)

State and prove Bayes' theorem using the theorem of total probability. (6 marks)

Bag I contains 3 red and 4 black balls and bag II contains 4 red and 5 black balls. One ball is transferred from bag I to bag II and then a ball is drawn from bag II. It is red. Find the probability that the transferred ball was black. (6 marks)

A random variable X has P(X = x) = kx for x = 1, 2, 3, 4 and 0 otherwise. Find k, P(X < 3), P(X >= 2) and the mean of X. (6 marks)