CBSE Class 10-Mathematics: Chapter –15 Probability Part 14

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Question 2:

A dice is thrown once. Find the probability of getting:

(i) A prime number.

(ii) A number lying between 2 and 6.

(iii) An odd number.

Answer:

Total number of favourable outcomes of throwing a dice

(i) On a dice, the prime numbers are and 5.

Therefore, favourable outcomes

Hence P (getting a prime number)

(ii) On a dice, the number lying between and 6 are .

Therefore, favourable outcomes

Hence

(iii) On a dice, the odd numbers are and .

Therefore, favourable outcomes

Hence P (getting an odd number)

Question 3:

A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result, i.e., three heads or three tails and loses otherwise. Calculate the probability that Hanif will lose the game.

Answer:

The outcomes associated with the experiment in which a coin is tossed thrice:

HHH, HHT, HTH, THH, TTH, HTT, THT, TTT

Therefore, Total number of favourable outcomes

Number of favourable outcomes

Hence required probability

Question 4:

A die is numbered in such a way that its faces show the numbers . It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws:

few values of the total score

Few Values of the Total Score

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Answer:

Complete table is as under:

The total score on the two throws

The Total Score on the Two Throws

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It is clear that total number of favourable outcomes

(i) Number of favourable outcomes of getting total score even are

Hence P (getting total score even)

(ii) Number of favourable outcomes of getting total score 6 are 4

Hence P (getting total score 6)

(iii) Number of favourable outcomes of getting total score at least 6 are 15

Hence P (getting total score at least 6)

Question 5:

18 cards numbered 1, 2, 3, …18 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probabilities that the card bears

(i) an even number

(ii) a number divisible by 2 or 3

Answer:

Total no. of possible outcomes = 18

(i) Favorable cases are 2,4,6,8,10,12,14,16,18 i.e., 9 in number

Required probability

(ii) Favorable cares are i.e., in number

Required probability