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QUESTION: 1

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

Solution:

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

Solution:

QUESTION: 3

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

Solution:

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

Solution:

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

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:

Solution:

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

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

Solution:

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

QUESTION: 7

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

Solution:

QUESTION: 8

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

Solution:

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

Solution:

QUESTION: 10

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

Solution:

QUESTION: 11

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

Solution:

QUESTION: 12

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

Solution:

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.

Solution:

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

QUESTION: 14

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

Solution:

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

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

Solution:

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

QUESTION: 16

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

Solution:

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

QUESTION: 17

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

Solution:

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

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

Solution:

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

QUESTION: 19

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

Solution:

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

Solution:

QUESTION: 21

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

Solution:

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

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

Solution:
Standard=1000-100=900

probaility=900/1000

=9/10

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:

Solution:

QUESTION: 24

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

Solution:

QUESTION: 25

The probability that a leap year has 53 Sundays is

Solution:

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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