# CBSE Class 10-Mathematics: Chapter – 15 Probability Part 14 (For CBSE, ICSE, IAS, NET, NRA 2023)

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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:

**Answer**:

Complete table is as under:

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