# Free Probability 03 Practice Test - 10th Grade

### Question 1

The sum of probabilities of two mutually exclusive events will always be 1.

True

False

#### SOLUTION

Solution :B

The sum of probabilities of two mutually exclusive events need not be always 1.

For example, consider the events “getting a prime number”, and “getting a composite number” for the experiment of rolling a die. They are mutually exclusive, but the sum of their probabilities is less than 1.

Favorable outcomes for prime no. = 2 , 3, 5

Favorable outcomes for composite no. = 4, 6

P(getting a prime no.) =36=12

P(getting a composite no.) =26=13

12+13≠1. So The sum of probabilities of two mutually exclusive events need not be always 1.

### Question 2

State whether the given statement is true or false:

There are 11 outcomes for the sum of two values obtained on rolling two dice.

True

False

#### SOLUTION

Solution :A

The sum of values on rolling two dice can be any integer value between 2 and 12. Hence, there are 11 outcomes.

### Question 3

If an unbiased die is thrown 5 times and every throw resulted in a 6 , what is the probability of getting a 6 on the sixth throw?

less than 16

16

In between 16 to 1

1

#### SOLUTION

Solution :D

Total number of trials = 5

Number of trials which resulted in '6' = 5

∴Experimental Probability, P(E)

=Number of trials in which the event happenedTotal number of trials

=55

=1

### Question 4

What is the probability of getting a sum of 7 on two rolls of a die?

712

111

16

23

#### SOLUTION

Solution :C

The total possible outcomes when a die is rolled twice are:

1 2 3 4 5 6 11,11,21,31,41,51,622,12,22,32,42,52,633,13,23,33,43,53,644,14,24,34,44,54,655,15,25,35,45,55,666,16,26,36,46,56,6

Total number of outcomes = 36

Number of ways to get sum as 7 = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

= 6

P(getting sum as 7)=Favourable outcomesTotal possible outcomes

=Outcome having same numbersTotal Outcomes

=636

= 16

### Question 5

What is the probability of getting a sum of 13 when rolling a pair of dice?

0

113

112

111

#### SOLUTION

Solution :A

The highest sum possible when rolling a pair of dice is 12(getting 6 on both dies). So getting a sum of 13 is an impossible event. Hence, the probability is 0.

### Question 6

The probability of picking the letter K if you pick a random letter from the word TREKKING is x4. x is

#### SOLUTION

Solution :The word TREKKING has 8 characters of which 2 are favourable. Hence, the probability is 28 = 14.

### Question 7

Indians , Egyptians , Europeans and Australians are residing in a village of area 200 km2. If the area is equally divided between the four countries, what is the probability that a particular person who lands in the village, finds himself in the area occupied by either Indians or Europeans?

0.60

0.33

0.45

0.50

#### SOLUTION

Solution :D

Each country occupies an area of 50km2

Probability that the person lands on a land occupied by Indians or Europeans = (50+50)200 = 12 = 0.50

### Question 8

5 defective glasses are accidentally mixed with 20 good ones. The good glasses and the defective ones look the same from the outside. If a glass is chosen at random, what is the probability that the chosen glass is good?

38

45

35

25

#### SOLUTION

Solution :B

Given, total number of glasses =25(20+5)

⇒ Total number of outcomes =25

Let E be the event of getting good glass.

Number of good ones =20

⇒ Number of favourable outcomes =20

Probability P(E)=Number of outcomes favourable to ENumber of all possible outcomes of the experiment

=2025=45

∴ The probability of getting a good glass is 45.

### Question 9

A card is drawn at random from a well-shuffled deck of 52 cards.What is the probability that the card drawn is a diamond?

12

13

14

15

#### SOLUTION

Solution :C

Given,

Total number of outcomes = 52

Number of diamonds = 13

Probability of an event, P(E) = =number of favourable outcomestotal number of outcomes

P (getting a card of diamond) = 1352=14

Therefore, probability of getting a card of diamond is 14 .

### Question 10

What is the probability of getting a sum of 7 on rolling a pair of dice?

712

111

16

23

#### SOLUTION

Solution :C

Given,

Sample space for rolling a pair of dice = S { (1,1) , (1,2) , (1,3) , (1,4), (1,5), (1,6) ,

(2,1) , (2,2) , (2,3) , (2,4) , (2,5) , (2,6) ,

(3,1) , (3,2) , (3,3) , (3,4) , (3,5) , (3,6) ,

(4,1) , (4,2) , (4,3) , (4,4) , (4,5) , (4,6) ,

(5,1) , (5,2) , (5,3) , (5,4) , (5,5) , (5,6) ,

(6,1) , (6,2) , (6,3) , (6,4) , (6,5) , (6,6) }

⇒ Total number of outcomes = 36

From the sample space, (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1) gives sum of 7.

⇒ Number of favourable outcomes = 6

Probability of an event, P(E) = number of favourable outcomestotal number of outcomes

P ( getting sum 7) =636=16

Therefore, the probability of getting a sum of 7 on rolling a pair of dice is 16 .