EXERCISE 25A

(1) (i) A coin is tossed. What are all possible outcomes?

Ans: All possible outcomes are Head (H) and Tail (T).

(ii) Two coins are tossed simultaneously. What are all possible outcomes?

Ans: HH, HT, TH, TT.

(iii) A die is thrown. What are all possible outcomes?

Ans: 1, 2, 2, 4, 5 and 6.

(iv) From a well- shuffled deck of 52 cards, one card is drawn at random. What is the number of all possible outcomes?

Ans: It has 13 cards of each suit, name spades, hearts and diamonds.

Cards of spades and clubs are black cards

Cards of hearts and diamonds are red cards.

There are 4 honours of each unit.

There are kings, queens and Jacks. These are all called face cards.

(2) In a single throw of a coin, what is the probability of getting a tail?

Solution: Total number of all possible outcomes = 2

Number of tails = 1

∴ P(getting tail) = ½.

(3) In a  single throw of two coins, find the probability of getting (i) both tails, (ii) at least 1 tail, (iii) at the most 1 tail.

Solution:  Total number of all possible outcomes = 4.

(i) Getting both tails TT.

Number of such outcomes = 1

∴ P(getting both tails) = ¼.

(ii) Getting at least 1 tail means HT, TH, TT.

Number of such outcomes = 3.

∴ P(Getting at least 1 tail) = ¾.

(iii) Getting at the most 1 tail means TH, HT, TT

Number of such outcomes = 3.

∴ P(Getting at least 1 tail) =3/4 .

(4) A bag contains 4 white and 5 blue balls. They are mixed thoroughly and one ball is drawn at random. What is the probability of getting (i) a white ball? (ii) a blue ball?

Solution: (i) Number of white balls = 4

∴ P = 4/9

(ii) Number of blue balls = 5

∴ P = 5/9.

(5) A bag contains 5 white, 6 red and 4 green balls. One ball is drawn at random. What is the probability that the ball drawn is (i) green? (ii) White? (ii) non – red?

Solution: Total number of ball = (5 + 6 + 4) = 15.

(i) Number of green balls = 4

∴ P = 4/15.

(ii) Number of white balls = 5

∴ P = 5/15 = 1/3.

(ii) Number of non-red balls = (4+5) = 9

∴ P = 9/15 = 3/5.

(6) In a lottery, there are 10 prizes and 20 blanks. A ticket is chosen at random. What is the probability of getting a prize?

Solution: Number of lottery = (10 + 20) = 30.

Number of getting prize = 10.

∴ P = 10/30 = 1/3.

(7) It is known that a box of 100 electric bulbs contains 8 defective bulbs. One bulb is taken out at random from the box. What is the probability that the bulb drawn is (i) defective? (ii) non-defective?

Solution: Number of total bulbs = 100.

(i) Number of defective bulbs = 8.

∴ P = 8/100 = 2/25.

(ii) Number of non-defective = 100 – 8 = 92

∴ P= 92/100 = 23/25.

(8) A die is thrown at random. Find the probability of getting (i) 2, (ii) a number less than 3, (iii) a composite number, (iv) a number not less than 4.

Solution: In throwing a die, all possible outcomes are 1, 2, 3, 4, 5, 6.

∴ number of all possible outcomes = 6.

(i) Number of getting 2 = 1

∴ P = 1/6 = 1/3.

(ii) number less than 3 = 1, 2 = 2

∴ P = 2/6 = 1/3.

(iii) a composite number= 4, 5

∴ P = 2/6 = 1/3

(iv) a number not less than 4 = 4, 5, 6

∴ P = 3/6 = ½.

(9) In a survey of 200 ladies, it was found that 82 like coffee while 118 dislike it. From these ladies, one is chosen at random. What is the probability that the chosen lady dislike coffee?

Solution: Number of total ladies = 200.

Number of  dislike coffee = 118

∴ P = 118/200 = 59/100.

(10) A box contains 19 balls bearing numbers 1, 2, 3, …. 19 respectively. A ball is drawn at random from the box. Find the probability that the number on the ball is (i) a prime number, (ii) an even number, (iii) a number divisible by 3.

Solution: Number of total balls = 19.

(i) Prime numbers = 2, 3, 5, 7, 11, 13, 17, 19 = 8

∴ P = 8/19

(ii) Even numbers = 2, 4, 6, 8, 10, 12, 14, 16, 18

∴ P = 9/19.

(iii) Number divisible by 3 = 3, 6, 9, 12, 15, 18

∴ P = 6/19.

(11) One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is (i) a king, (ii) a spade, (iii) a red queen, (iv) a black 8.

Solution: Total number of cards = 52

(i) Number of king = 4

∴ P = 4/52 = 1/13.

(ii) Spade = 13/52 = ¼.

(iii) red queen = 2

∴ P = 2/52 = 1/26.

(iv) Black 8 = 2

∴ P = 2/52 = 1/26.

(12) One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is (i) a 4, (ii) a queen, (iii) a black card.

Solution: Total number of cards = 52.

(i) Number of 4 = 4

∴ P = 4/52 = 1/13.

(ii)Number of queen = 4

∴ P = 4/52 = 1/13.

(iii) Number of black card = 13 +13 = 26

∴ P = 26/52 = ½.