Probability quiz

The probability of an impossible event is:

If P(E) = 0.05, then P(not E) is:

The probability of getting a prime number when a die is thrown once is:

One card is drawn from a deck of 52 cards. The probability that it is an ace is:

Which of the following cannot be the probability of an event?

When two coins are tossed together, the probability of getting at least one head is:

A bag contains 3 red balls and 5 black balls. The probability of drawing a red ball is:

The probability that a leap year chosen at random has 53 Sundays is:

The sum of the probabilities of all the elementary events of an experiment is:

Two dice are thrown together. The probability that the sum is less than or equal to 3 is:

A die is thrown once. Find the probability of getting (i) a number greater than 4 (ii) a number less than or equal to 4. (2 marks)

It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday? (2 marks)

A lot of 20 bulbs contains 4 defective ones. One bulb is drawn at random. What is the probability that it is defective? (2 marks)

12 defective pens are accidentally mixed with 132 good ones. One pen is taken out at random. Find the probability that it is a good one. (2 marks)

Why is tossing a coin considered a fair way of deciding which team should get the ball at the beginning of a football match? (2 marks)

A die has its six faces marked A, B, C, D, E, A. It is thrown once. What is the probability of getting (i) A (ii) D? (2 marks)

One card is drawn from a deck of 52 cards. Find the probability of getting the jack of hearts and a red face card. (2 marks)

A child has a die whose six faces show the letters of the word MANGO plus the letter E (M, A, N, G, O, E). Find the probability of getting a vowel. (2 marks)

Cards numbered 2 to 101 are placed in a box. One card is drawn at random. Find the probability that it bears an even number. (2 marks)

A fish tank has 5 male fish and 8 female fish. A fish is taken out at random. What is the probability that it is a male fish? (2 marks)

A box contains 12 balls of which x are black. If one ball is drawn at random, the probability that it is black is p. If 6 more black balls are put into the box, the probability of drawing a black ball becomes 2p. Find x. (3 marks)

A jar contains 24 marbles, some green and others blue. If a marble is drawn at random, the probability that it is green is 2/3. Find the number of blue marbles in the jar. (3 marks)

Two dice, one blue and one grey, are thrown at the same time. Find the probability that the product of the numbers on the top faces is (i) 6 (ii) 12 (iii) 7. (3 marks)

A carton of 24 bulbs contains 6 defective bulbs. One bulb is drawn at random and found to be defective; it is not replaced. Another bulb is then drawn at random from the rest. Find the probability that this second bulb is not defective. (3 marks)

A game consists of tossing a one-rupee coin 3 times and noting its outcome each time. Find the probability of getting (i) exactly one head (ii) at least two heads (iii) no head. (3 marks)

Read the passage and answer the questions. At a school fair, a stall has a box containing 20 tickets numbered 1 to 20. A visitor draws one ticket at random and wins a prize if the number is a multiple of 3 or a multiple of 5. (i) How many tickets are multiples of 3, and how many are multiples of 5? (ii) How many tickets win a prize? Note that some tickets are multiples of both. (iii) Find the probability of winning a prize and of not winning. (5 marks)

Read the passage and answer the questions. A quality inspector at a factory checks a lot of 144 ball pens, of which 20 are defective. A customer will buy a pen only if it is good. The shopkeeper draws one pen at random and gives it to the customer. (i) Find the probability that the customer will buy the pen. (ii) Find the probability that the customer will not buy it. (iii) Verify that the two probabilities add up to 1, and name the type of events. (5 marks)

Read the passage and answer the questions. In a cricket quiz, cards with the names of 52 players are made, 13 from each of four teams A, B, C and D. Within each team the cards are numbered 1 to 13. One card is drawn at random. (i) Find the probability that the player belongs to team A. (ii) Find the probability that the card bears number 13. (iii) Explain how this situation is similar to drawing a card from a pack of 52 playing cards. (5 marks)

Read the passage and answer the questions. Ravi and Neha play a game with two dice. Ravi wins if the sum of the numbers is 7, and Neha wins if the sum is 10 or more. (i) Find the number of outcomes favourable to Ravi. (ii) Find the number of outcomes favourable to Neha. (iii) Who has a better chance of winning? Justify with probabilities. (5 marks)

Read the passage and answer the questions. A survey of 200 families in a colony shows that 40 families have no car, 120 families have one car and 40 families have two cars. A family is chosen at random to receive a gift voucher. (i) Find the probability that the family has exactly one car. (ii) Find the probability that the family has at least one car. (iii) Find the probability that the family has two cars, and check that the probabilities of the three types of family add up to 1. (5 marks)

Distinguish between experimental and theoretical probability, giving one example of each. Write all 36 outcomes of throwing two dice and complete the probability of each sum from 2 to 12. Draw a bar diagram showing these probabilities and identify the most likely sum. (6 marks)

One card is drawn from a well-shuffled deck of 52 cards. Describe the composition of the deck (suits, colours and face cards). Find the probability of getting (i) a king of red colour (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) the queen of diamonds. (6 marks)

Five cards, the ten, jack, queen, king and ace of diamonds, are well shuffled with their faces downward. One card is picked at random. (i) What is the probability that it is the queen? (ii) If the queen is drawn and put aside, what is the probability that the second card picked is an ace, and a queen? Draw a simple diagram showing the cards before and after the first draw. (6 marks)

A bag contains red, blue and yellow balls, all of the same size. The probability of drawing a red ball is 1/4 and that of a blue ball is 1/3. (i) Find the probability of drawing a yellow ball. (ii) If the bag has 10 yellow balls, find the total number of balls and the number of balls of each colour. Draw a pie chart showing the share of each colour. (6 marks)

Explain, with examples, the terms elementary event, complementary event, sure event and impossible event. Prove that for any event E, P(E) + P(not E) = 1, and use it to find the probability that a number selected at random from 1 to 30 is not a prime number. (6 marks)