Please refer to Probability HOTs Class 10 Mathematics provided below with Probability. All HOTs for Class 10 Mathematics with answers provided below have been designed as per the latest syllabus and examination petter issued by CBSE, NCERT, KVS. Students of Standard 10 Mathematics should learn the solved HOTS for Class 10 Mathematics provided below to gain better marks in examinations.

**Probability Class 10 Mathematics HOTs**

**Questions of 1 Mark**

**Question.****Find the probability of getting 53 Fridays in a leap year.**

## Answer

A leap year consist of 52 weeks and 2 extra days.

n(S) = 7 , n(E) = 2 , P(E) = 2/7

**Question.** A die is thrown once. Find the probability of getting multiple of 2 or 3.

## Answer

(1) S = {1,2,3,4,5,6} n(S) = 6

E = {2,3,4,6} n(E) = 4 P(E) = 4/6 = 2/3

**Question.** A bag contain 4 red, 5 black and 6 white balls & ball is drawn from the bag at random. Find the probability that ball drawn is**a) Not black ****b) Red or White**

## Answer

**Question.** Write a sample space when two coins are tossed simultaneously?

## Answer

S = {HH,HT,TH,TT}

**Question.** The probability that it will rain tomorrow is 0.85. What is the probability that it will not rain tomorrow ?

## Answer

P(E) = 0.85

P(E) = 1 – P(E) = 1 – P(E) = 1 – .085 = 0.15

**Question.** In a single throw of two dice, find the probability of not getting the same number on the two dice.

## Answer

**Question.** A card is drawn at random from a well shuffled pack of playing cards.

Find the probability that the card drawn is

a) Red and a queen

b) Either a king or jack

## Answer

**Question.** What is the probability of

a) A sure event

b) Impossible event

## Answer

(a) P(S) = 1 (b) P(2) = 0

**Question.** 15 cards numbered 1,2,3………15 are put in a box and mixed thoroughly & card is drawn at random from the box. Find the probability that the card drawn is

a) neither prime nor odd

b) a number which is a perfect square.

## Answer

**Question.** Two coins are tossed simultaneously once. What is the probability of getting

a) Exactly one head

b) No head

## Answer

**Question.** Two coins are tossed simultaneously once. Find the probability of getting

a) at least one head and one tail.

b) at most 2 heads.

## Answer

**Question.** A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears.

a) not divisible by 5 or 10.

b) two digit number.

## Answer

**Question.** A bag contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball. If more black balls are put in the box the probability of drawing a black ball is now double of what it was before. Find x

## Answer

**Question.** In a single throw of two dice, find probability of getting

a) doubles**b) a total of 11**

## Answer

**Question.****One card is drawn from well-shuffled pack of 52 cards. Find the probability of gettinga) the jack of hearts**

**b) a face card.**

## Answer

(1) 1/52 (2) 12/52 = 3/13 (Jack, King & Queen)

**Question.** Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday) each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on

i) the same day?**ii) consecutive day?****iii) Different day?**

## Answer

S= {Tue, Wed, Thur, Fri, Sat} n(S) = 25

(1) 5/25 = 1/5 (2) 8/25 (3) 20/25 = 4/5

**Question.** All the three face cards of spade are removed from a well shuffled pack of 52 cards & card is drawn from the remaining pack. Find the probability of getting

a) a black face card**b) a queen of diamond****c) a spade****d) a black card**

## Answer

(1) 9/49 (2) 1/49 (3) 10/49 (4) 23/49

**Question.****A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuvi will buy a pen if it is good, but will not buy it if it is defective. The shopkeeper draws one pen at random and gives it to him. What is the probability thati) She will buy it**

**ii) She will not buy it**

## Answer

20 Defected & 124 Non-Defected

(1) 124/144 = 31/36 (2) 20/144 = 5/36

**Question.****A letter is chosen at random from the letters of the word “ASSASSI NATION” and the probabilities that the letter chosen is ai) vowelii) consonant**

## Answer

A,A,I,A,I,O = 6’s Vowels S,S,S,S,N,T,N = 7’S Constants

(1) 6/13 (2) 7/13

**Question.** Savita and Hamida are friends what is the probability that both will have

i) the same birthday?**ii) different birthday?**

## Answer

(1) 1/365 (2) 364/365