# Free Probability 01 Practice Test - 10th Grade

### Question 1

State whether the given statement is true or false:

A bag contains 4 red and 8 blue marbles. A marble is drawn at random. The probability of drawing red is 13.

True

False

#### SOLUTION

Solution :A

There are 4 red marbles out of a total of 12 marbles. So, the probability of drawing red is 412 = 13.

### Question 2

What is the probability that the minute and hour hands of a clock will form an acute angle at any given time?

P ≤ 0.25

P < 0.5

P = 0.5

P > 0.5

#### SOLUTION

Solution :B

The number of times in a period of 12 hours the hands of the clock will form an acute angle will be the same as that for obtuse angle. So, you would think that the probability is 12. But if you take into account the number of times when the hands are alligned ( 0∘), hands are at right angles and hands are facing in opposite directions ( 180∘), then the probability would be slightly less than 0.5.

### Question 3

If a coin is tossed 3 times, what is the probability of getting a tail each time?

18

116

14

16

#### SOLUTION

Solution :A

If a coin tossed thrice, the total possible outcomes = {HHH, HHT, HTT, HTH, THH, TTH, THT, TTT}.

= 8

Number of cases of getting tail each time = {TTT}

= 1

The probability of getting tail each time = Number of favourable casestotal possible outcomes

= 18

### Question 4

A card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a spade?

18

0.33

14

0.25

#### SOLUTION

Solution :C and D

Sample space = total number of cards in deck = 52.

Favorable outcome (getting a spade) = 13.

Hence, P(getting a spade) = 1352 = 14.

### Question 5

A bag contains 100 identical marble stones numbered from 1 to 100. What is the probability of drawing a marble having a number divisible by both 4 and 5?

125

225

220

120

#### SOLUTION

Solution :D

Numbers divisible by 4 and 5 both = 20, 40, 60, 80, 100.

Hence P = Favourable outcomesTotal outcomes = 5100= 120

= 120

### Question 6

Sum of probabilities of all outcomes in an experiment is

#### SOLUTION

Solution :The sum of the probabilities of all the elementary events of an experiment is 1.

### Question 7

You are given a dart board of radius R cm. What is the probability that you hit the bull's eye of radius r cm?

r2R2

rR

Rr

1

#### SOLUTION

Solution :A

Area of board = π R2

Area of bull's eye = π r2

Here, we shall use the concept of geometric probability as the number of outcomes are not finite.

The probability of hitting the bull's eye

=Area of the bull's eyeArea of the board=π.r2π.R2 = r2R2

### Question 8

Which of the following cannot be the probability of an event?

#### SOLUTION

Solution :B

The probability of an event E, P(E)=favourable no. of outcomestotal no. of outcomes

Since the favourable no. of outcomes are always less than or equal to the total no. of outcomes, P(E)≤1.

### Question 9

A book has pages numbered from 1 to 85. What is the probability that the sum of the digits on the page is 8, if a page is chosen at random?

685

785

985

885

#### SOLUTION

Solution :C

Total number of pages in the book = 85

Favorable outcomes are: 8, 17, 26, 35, 44, 53, 62, 71, 80.

∴ No. of favorable outcomes = 9

Let E be the event of getting sum of the digits on the page is 8.

Probability P(E) = Number of outcomes favorable to ENumber of all possible outcomes of the experiment=985

### Question 10

A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 23. Find the number of blue marbles in the jar.

12

16

11

8

#### SOLUTION

Solution :D

Given: P(green marble)=23

Since there are 24 marbles, therefore the sample space will be 24 (i.e. the denominator must be 24.)

Let us assume there are x number ofgreen marbles in the jar.

For an event E, probability P(E)=Number of outcomes favorable to ENumber of all possible outcomes of the experiment

⇒P(green marbles)=23=x24

⇒x=16

It implies that there are 16 green marbles in a jar of 24 marbles.

∴Number of blue marbles =24−16=8.