# NCERT Class 10 Chapter 13 Probability CBSE Board Sample Problems Short Answer (For CBSE, ICSE, IAS, NET, NRA 2023)

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## Question

A game of chance consists of spinning an arrow on a circular board, divided into 8 equal parts, which comes to rest pointing at one of the numbers 1,2, 3, … , 8 which are equally likely outcomes. What is the probability that the arrow will point at an odd number

a number greater than 3

a number less than 9.

### Solution

Total possible outcomes when the arrow points at one of the numbers are 8.

Favourable outcomes when the required number is odd are 1, 3,5, 7, i.e.. 4 outcomes.

Favourable outcomes when the required number is more than 3 are 4, 5, 6,7, 8, i.e.. 5 outcomes.

Favourable outcomes when the required number is less than 9 are 1.2, 3, 4, 5,6, 7,8 i.e.. 8 outcomes

=

=

## Question

A game consist of tossing a one-rupee coin 3 times and nothing the outcome each time.

Ramesh will win the game if all the show the tosses same result, (i.e.. either all three heads or all three tails) and loses the game otherwise. Find the probability that Ramesh will lose the game.

### Solution

When three coins are tossed together, then total outcomes are HHH, HHT, HTT, TTT, TTH,

THH, HTH, THT Total possible cases = 8

Favourable cases to win the game are HHH or TTT, i.e.. two cases.

P (Ramesh will win the game) =

Required probability = P (Ramesh will loose the game)

## Question

There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card: is divisible by 9 and is a perfect square.

Is a prime number greater than 80.

### Solution

Total possible cases

Favourable cases when number is a perfect square and is divisible by 9 are 9,36 and 81.

So, number of favourable cases = 3

Favourable cases the prime numbers greater than 80 are 83,89 and 97

So, number of favourable cases

Required probability

## Question

From a pack of 52 playing cards, Jacks, Queens and Kings of red colour are removed.

From the remaining, a card is drawn at random. Find the probability that drawn card is: a black king.

a card of red colour.

a card of black colour.

### Solution

Removed red colour cards

Remaining cards

Number of black kings

P (a black king)

Number of red colour cards

Remaining red colour cards

P (a card of red colour)

Number of black cards = 26

P (a black colour card)

## Question

Three different coins are tossed together. Find the probability of getting exactly two heads at least two heads at least two tails.

### Solution

Possible outcomes when three coins are tossed HHH, HHT, HTT. UT, THH, TTH, HTH, THT

Number of exactly two heads are HHT, HTH and THH.

In case of at least two heads, outcomes are HHT, HTH, THH and HHH.

In case of at least two tails, outcomes are TTH. THT, HTT and TU.

P (at least two tails)

## Question

A box consists of loo shirts of which 88 are good, 8 have minor defects and 4 have major defects. Ramesh, a shopkeeper will buy only those shirts which are good but ‘Kewal’ another shopkeeper will not buy shirts with major defects. A shirt is taken out of the box at random. What is the probability that Ramesh will buy the selected shirt?

‘Kewal’ will buy the selected shirt?

### Solution

When one shirt is taken out, then number of total possible outcomes

Ra mesh will purchase when shirt is good,

Favourable outcomes = number of good shirts

Kewal will buy shirt if a shirt is not having major defect.

Number of favourable outcomes = Number of shirts without major defect

## Question

Two different dice are thrown together. Find the probability of: getting a number greater than 3 on each die.

Getting a total of 6 or 7 of the numbers on two dice

### Solution

When two dice are thrown together total possible outcomes

Favourable outcomes when both dice have number more than 3 are

, i.e.. 9 outcomes.

Favourable outcomes when sum of the numbers appearing on the dice is 6 or 7 are, i.e..

outcomes.

P (a total of 6 or 7)

P (a number greater than 3 on each due) =

## Question

In a single throw of a pair of different dice, what is the probability of getting a prime number on each dice?

A total of 9 or 11?

### Solution

Total possible cases when two dice are thrown together

Favourable cases when both numbers are prime are

i.e.. 9 outcomes

P (a prime number on each dice)

(ii) Favourable cases when sum of numbers are 9 or 11 are

i.e.. 6 outcomes

P (a total 9 or 11)

## Questions

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball. Determine the number of blue balls in the bag.

### Solution

Let the number of blue bails is the bag be x

Then total number of balls is the bag

: . Number of all possible outcomes

Number of outcomes favourable to the event of drawing a blue ball

Probability of drawing a blue ball

Similarly, Probability of drawing a red ball =

## Question

A bag contains 8 red balls and x blue balls, the odd against drawing a blue ball are 2: 5.

What is the value of X?

### Solution

No of blue balls be x

No. of red balls be 8 Total no. of balls

Probability of drawing blue bails =

Probability of drawing red balls =

## Question

A box 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 6 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.

### Solution

There are 12 balls in the box.

Therefore, the total number of possible outcomes = 12

The number of favourable outcomes = x

Probability of the event =

Therefore (Getting a black ball) =

If 6 more balls put in the box, then

Total number of favourable outcomes

and number of favourable outcomes

(Getting a black ball)

According to question,

## Question

A die is rolled, find the probability of getting

(a) A number greater than 8

(b) a number less than 10

### Solution

(a) P (number greater than 8) = 0 as its an impossible event

(b) P (number less than 10) = 1 as it՚s a sure event

## Question

Find the probability of having S Mondays in the month of August.

### Solution

There are 4 complete weeks and 3 extra days. The probability for August to have 5 Mondays is

## Question

A bag contains tickets numbered from 10 to 50. One ticket is drawn at random. Find the probability that the number on the card is (a) prime (b) a perfect square.

### Solution

No of tickets

The prime numbers are 11, 13, 17, 19, 23, 29, 31, 37,41, 43, and 47

P (prime) =

P (perfect square)

## Question

A bag contains 24 balls of which x are red, 2x are white, 3x are blue. A ball is selected at random. What is the probability that it is?

Not red

White

P (not red)

P (white)

## Question

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

## Question

A die is thrown twice. What is the probability that:

(a) 3 will not come up either time?

(b) 3 will come up at least once?

### Solution

Let E be the event that 3 will come up at least once. When a die is thrown twice.

Favorable outcomes are

(a) P (3 will not come up either time) = 1 - (3 Will come up at least once)

(b) P (3 Will come up at least once)

## Question

The quality control officer at a tire factory reported that 20 tires were defective out of a sample of 10.000 tires. A tire is selected, what are the chances that the tire selected is not defective?

### Solution

Total number of tires = 10000

Number of defective tires = 20

P (Defective tires)

P (non-defective tire)