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Test: Applications of Probability - Class 10 MCQ


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25 Questions MCQ Test Mathematics (Maths) Class 10 - Test: Applications of Probability

Test: Applications of Probability for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The Test: Applications of Probability questions and answers have been prepared according to the Class 10 exam syllabus.The Test: Applications of Probability MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Applications of Probability below.
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Test: Applications of Probability - Question 1

Harry tosses two coins simultaneously. The probability of getting at least one head is​

Detailed Solution for Test: Applications of Probability - Question 1

When Harry tosses two coins simultaneously, there are four possible outcomes:

  1. Heads on both coins (HH)
  2. Heads on the first coin and tails on the second (HT)
  3. Tails on the first coin and heads on the second (TH)
  4. Tails on both coins (TT)

To calculate the probability of getting at least one head, we need to find the probability of all outcomes that have at least one head (i.e., exclude the outcome where there are no heads, which is TT).

The favorable outcomes are:

  • HH
  • HT
  • TH

There are 3 favorable outcomes out of the 4 possible outcomes.

Thus, the probability of getting at least one head is:

P(at least one head)=3/4 

Therefore, the correct answer is b) 3/4.

Test: Applications of Probability - Question 2

An urn contains lottery tickets numbered from 1 to 100. If a ticket is selected at random, then the probability that it is a perfect square is​

Detailed Solution for Test: Applications of Probability - Question 2

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Test: Applications of Probability - Question 3

If the probability of winning a game is 0.3, the probability of losing it is​

Detailed Solution for Test: Applications of Probability - Question 3

Test: Applications of Probability - Question 4

Three face cards of spade are removed from a well shuffled pack of 52 cards and a card is drawn from the remaining pack. The probability of getting a black face card is​

Detailed Solution for Test: Applications of Probability - Question 4

Three face cards from spades have been removed.
Total cards=52-3=49
Total No of black face cards=3+3(3 in each spades and clubs)
Remaining black face cards=6-3=3
Probability of getting black face card=  no. of favourable outcomes/ total no. of outcomes=3/49

Test: Applications of Probability - Question 5

A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag. The probability that it bears a two digit number is:

Detailed Solution for Test: Applications of Probability - Question 5

Total number of outcomes=90-1=89
No. of favourable outcomes = Total outcomes - One digit number =89-8=81
Probability of having a two digit number=Total number of outcomes/No. of favourable outcomes=81/89

Test: Applications of Probability - Question 6

A card is drawn from a well-shuffled deck of 52 playing cards. The probability that the card will not be an ace card is​

Detailed Solution for Test: Applications of Probability - Question 6

Total no. of outcomes=52
No. of ace cards=4
No. of non-ace cards=48
Probability of getting a non-ace card = No. of favourable outcomes / total no. of outcomes
=48/52=12/13

Test: Applications of Probability - Question 7

Three unbiased coins are tossed. What is the probability of getting at most two heads?

Detailed Solution for Test: Applications of Probability - Question 7

Test: Applications of Probability - Question 8

Two coins are tossed simultaneously once. Find the probability of getting at least one head and one tail.

Detailed Solution for Test: Applications of Probability - Question 8

Test: Applications of Probability - Question 9

A bag contains 3 white and 5 red balls. If a ball is drawn at random, the probability that the drawn ball is red is​

Detailed Solution for Test: Applications of Probability - Question 9

Explanation: Total number of balls = 3 white + 5 red = 8 balls.

The number of red balls = 5.

Probability = (Number of red balls) / (Total number of balls) = 5/8.

So, the correct answer is Option D.

Test: Applications of Probability - Question 10

The probability that a consonant is selected from the English alphabet is

Detailed Solution for Test: Applications of Probability - Question 10

The English alphabet consists of 26 letters, with 5 vowels (A, E, I, O, U) and 21 consonants.


  • Number of consonants: 21
  • Total letters in the alphabet: 26

To find the probability of selecting a consonant, use the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

So, the probability = 21/26.

Thus, the correct answer is:

A: 21/26

Test: Applications of Probability - Question 11

Harmeet tosses two coins simultaneously. The probability of getting at least one head is​

Detailed Solution for Test: Applications of Probability - Question 11

Explanation: When two coins are tossed, the possible outcomes are:

  1. Head, Head (HH)
  2. Head, Tail (HT)
  3. Tail, Head (TH)
  4. Tail, Tail (TT)

The event "at least one head" includes the outcomes HH, HT, and TH. So, there are 3 favorable outcomes.

Total number of outcomes = 4 (HH, HT, TH, TT).

Probability = (Number of favorable outcomes) / (Total number of outcomes) = 3/4.

Test: Applications of Probability - Question 12

The probability of getting a number less than 5 in a single throw of dice is

Detailed Solution for Test: Applications of Probability - Question 12

Answer: Option B (2/3)

Explanation: The possible outcomes when a die is thrown are 1, 2, 3, 4, 5, and 6.

The numbers less than 5 are 1, 2, 3, and 4. So, there are 4 favorable outcomes.

Total number of outcomes = 6.

Probability = (Number of favorable outcomes) / (Total number of outcomes) = 4/6 = 2/3.

Test: Applications of Probability - Question 13

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 black face card.​

Detailed Solution for Test: Applications of Probability - Question 13

As three cards have been removed, there are now 49 cards in the deck.

As the three cards removed were the 3 spades face cards, there are only 3 black face cards left (the J, Q, K of clubs).

P ( black face card) = ( favourable outcomes ) / ( possible outcomes )

= 3 / 49

Test: Applications of Probability - Question 14

A fair die is cast in the game of ‘Ludo’. The probability of getting a score greater than 6 is

Detailed Solution for Test: Applications of Probability - Question 14

A fair dice has number 1,2,3,4,5,6 only . So there are no number greater than 6
No. of favourable outcomes=0
Total no. of outcomes=6
Probability of getting no. higher than 6=No. of favourable outcomes/Total no. of outcomes=0/6=0
 

Test: Applications of Probability - Question 15

Aarti selects a card from a pack of well shuffled 52 playing cards. She needs an ace to win the game. The probability of Aarti losing the game is​

Detailed Solution for Test: Applications of Probability - Question 15

P(E) = number of expected trials / total number of trials
A standard deck of cards has 52 cards.
Number of expected trials = 4 x 12 = 48 cards
Total number of trials = 52
Therefore, P(E) = 48/52
= 12/13

Test: Applications of Probability - Question 16

In a throw of a die, the probability of getting a prime number is​

Detailed Solution for Test: Applications of Probability - Question 16

The possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6}

Number of possible outcomes of a dice = 6

(i) Prime numbers on a dice are 2, 3, and 5.

Total prime numbers on a dice = 3

Probability of getting a prime number = 3/6 = 1/2

Test: Applications of Probability - Question 17

One card is drawn from a deck of 52 cards. The probability of drawing a black card is​

Detailed Solution for Test: Applications of Probability - Question 17

We have total cards = 52
4 categories=spades,clubs,diamonds and hearts
Spades and clubs are black cards
No. of favourable outcomes=13+13=26
Probability of getting a black card= no. of favourable outcomes/total no. of outcomes
=26/52=1/2

Test: Applications of Probability - Question 18

A bag has 9 red, 7 green and 4 blue balls. A student randomly selects a ball from the bag. The probability of not getting a blue ball is

Detailed Solution for Test: Applications of Probability - Question 18

Total number of balls in the bag=9+4+7=20 balls
No. of favourable outcomes=not getting blue ball= getting either the red ball or green ball=9+7=16
Probability of not getting blue ball = no. of favourable outcomes/total number of outcomes=16/20=4/5

Test: Applications of Probability - Question 19

What is the probability of getting a king when a card is drawn from a well shuffled deck of 52 playing cards?​

Detailed Solution for Test: Applications of Probability - Question 19

Test: Applications of Probability - Question 20

Cards each marked with one of the numbers 4, 5, 6 …20 are put in a box and mixed thoroughly. One card is drawn at random from the box. The probability of getting an even prime number is

Test: Applications of Probability - Question 21

A die is thrown once. Find the probability of getting a number that is either composite or prime.​

Detailed Solution for Test: Applications of Probability - Question 21

The possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6}

Number of possible outcomes of a dice = 6

Prime numbers on a dice are 2, 3, and 5.

Composite numbers on dice = 4, 6

Total prime numbers on a dice = 3

Total composite numbers on a dice  = 2

So, total (prime + composite) = 5

Probability of getting a number that is either prime or composite = 5/6

Test: Applications of Probability - Question 22

Out of a day’s production, which is 1000 machine parts, 100 were found to be sub-standard. The probability that a part selected at random being up to the standard is

Detailed Solution for Test: Applications of Probability - Question 22
Standard=1000-100=900
probaility=900/1000
             =9/10

Test: Applications of Probability - Question 23

From a well-shuffled pack of 52 cards, a card is drawn at random. The probability that it is a face card is:​

Detailed Solution for Test: Applications of Probability - Question 23

Explanation: In a deck of 52 cards, there are 3 face cards (Jack, Queen, King) in each of the 4 suits (hearts, diamonds, clubs, spades).

So, the total number of face cards = 3 face cards × 4 suits = 12 face cards.

Total number of cards = 52.

Probability = (Number of face cards) / (Total number of cards) = 12/52 = 3/13.

So, the correct answer is Option D.

Test: Applications of Probability - Question 24

One card is drawn from a deck of 52 cards. The probability of drawing a black card is

Detailed Solution for Test: Applications of Probability - Question 24

Explanation: A standard deck of 52 cards contains 26 black cards (13 spades and 13 clubs).

The total number of cards = 52.

The number of black cards = 26.

Probability = (Number of black cards) / (Total number of cards) = 26/52 = 1/2.

Test: Applications of Probability - Question 25

The probability that a leap year has 53 Sundays is​

Detailed Solution for Test: Applications of Probability - Question 25

There are 366 days in a leap year, i.e, 1 more than a normal year.

Now, 52 weeks make up 344 days (52 x 7 = 344)
That means that we already have 52 sundays for sure.

Then, we are left with 2 days. Now, these days can be any from a pair of- mon-tues,tues-wed,wed-thurs,thurs-fri,fri-sat,sat-sun,sun-mon. Here favourable cases are sat-sun and sun-mon i.e, 2 cases and total number of cases is 7.

So, Probability=number of favourable cases/Total number of cases.

Therefore, Probability= 2/7.

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