Q. A piggy bank contains hundred 50 p coins, fifty ₹ 1 coins, twenty ₹ 2 coins and ten ₹ 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, find the probability that the coin which fell (i) will be a 50p coin, (ii) will be of value more than ₹ 1, (iii) will be value less than ₹ 5, and (iv) will be a ₹ 1 or ₹ 2 coin.

  • Ans. Total number of coins = (100 + 50 + 20 + 10) = 180 (i) Possible number of outcomes of a 50 p coin falling out = 100
  • Hence, P(E) =100/180=5/9
  • (ii) Possible number of outcomes of a coin falling out having value more than ₹ 1 = (20 + 10) = 30
  • Hence, P(E) =30/180=1/6
  • (iii) Possible number of outcomes of a coin falling out having value less than ₹ 5 = (100 + 50 + 20) = 170
  • Hence, P(E) = 170/180/=17/18
  • (iv) Possible number of outcomes of a coin falling out having value either ₹ 1 or ₹ 2 = (50 + 20) = 70
  • Hence, P(E) =70/180=7/18 Ans.

Q. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is double that of a red ball, find the number of blue balls in the bag.

Ans. 10.

Q. A bag contains 12 balls out of which x are white. If one ball is drawn at random what is the probability that it will be white ? If six more white balls are put in the bag the probability of drawing a white ball doubles. Find x.

Ans. 1/4, 3.

Q. A child has a block in the shape of a cube with a letter written on each face (A, B, C, D, E, A).The cube is thrown once. What is the probability of getting (i) an A and (ii) a D?

  • Ans. (i) 1/3, (ii) 1/6·

Q. There are 40 students in Class X of a school of whom 25 are girls and 15 are boys. The class teacher, in order to select a class representative, writes down the names of all the students on same-sized pieces of cardboard and puts them in a box. Before drawing out a name, she stirs it well. What is the probability of the name being that of a (i) girl’s and (ii) a boy’s?

  • Ans. (i) 5/8, (ii) 3/8·

Q. Gopi buys a fish from a shop for his aquarium. The shopkeeper picks one at random from a tank containing 8 female fish and 5 male fish. What is the probability that the fish taken out is a male fish?

  • Ans. 5/13.

Q. A jar contains 24 marbles of which some are green and the rest are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3 · Find the number of blue marbles in the jar.

  • Ans. 8.

Q. A die is thrown. Find the probability of getting (i) a prime number, (ii) an even prime number, (iii) a number greater than 5 and (iv) a number lying between 2 and 6.

Ans. (i) 1/2

(ii) 1/6.

(iii) 1/6

(iv) 1/2

Q. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a red king, (ii) a face card, (iii) a red face card, (iv) a black queen, (v) a jack of hearts, and (vi) a spade.

Ans. (i) 1/26

(ii) 3/13

(iii) 3/26

(iv) 1/26

(v) 1/52

(vi) 1/4·

Q. A bag contains 3 red and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball is (i) red, (ii) black?

Ans. (i) 3/8

(ii) 5/8·

Q. Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any day as on another. What is the probability that both will visit the shop on (i) the same day, (ii) on different days and (iii) on consecutive days?

Ans. (i) 1/6

(ii) 5/6

(iii) 5/36·

Q. 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?

Ans. 0.008.

Q. (i) A lot of 20 electric bulbs contains 4 defective bulbs. One bulb is taken out at random from the box. What is the probability that the bulb drawn is defective ? (ii) Suppose the bulb is not defective and not replaced and another bulb is drawn from the lot, what is the probability that the second bulb is also not defective?

Ans. (i) 1/5

(ii) 15/19·

Q. A box contains 90 discs that are numbered from 1 to 90. If a disc is drawn at a random from the box, find the probability that it bears (i) a two-digit number, (ii) a perfect square number and (iii) a number divisible by 5.

Ans. (i) 9/10

(ii) 1/10

(iii) 1/5·

Q. A lot consists of 144 ball pens of which 20 are defective and others are good. Nuri will buy a pen if it is good but will not buy one if it is defective. The shopkeeper draws one pen at a random and gives it to her. Find the probability of Nuri’s buying and not buying it.

Ans. 31/36, 5/36·

Q. A lot consists of 144 pens of which 12 are defective and others are good. One pen is drawn out at random. Find the probability of the pen being a good one.

Ans. 19/18·

Q. An unbiased die is thrown. What is the probability of getting (i) a multiple of 3, (ii) an even number or a multiple of 3 and (iii) an odd number?

Ans. (i) 1/3

(ii) 2/3

(iii) 1/2·

Q. A box contains 4 green, 8 white and 5 red marbles. If a marble is drawn out at random from the box, what is the probability that it will be (i) red, (ii) white, and (iii) not green marble?

Ans. (i) 5/17

(ii) 8/17

(iii) 13/17·