# Free Probability 01 Practice Test - 9th Grade

In a cricket match, a batsman hit a boundary 6 times (out of 30 balls). Find the probability that next ball he plays is not a boundary.

A.

0.2

B.

0.4

C.

0.6

D.

0.8

#### SOLUTION

Solution : D

Total number of balls played = 30

Number of balls in which the batsman hit a boundary = 6

Number of balls in which he did not hit a boundary
= 30 – 6
= 24

Probability of not hitting a boundary=Number of balls in which he does not hit a boundaryTotal number of balls played=2430=0.8

Parts exiting an assembly line are inspected and categorized as good or bad (defective). In a batch of 100 parts, 8 were found to be defective.
What is the probability that a part drawn at random is defective?

A.

0.2

B.

0.02

C.

0.08

D.

0.8

#### SOLUTION

Solution : C

Number of parts exiting an assembly line which are bad(defective) = 8

Total number of parts passing the assembly line = 100

Probability of part being defective =Number of defective partsTotal number of parts

Probability of a part being defective =8100=0.08

Out of 50 students in a class taking a test, 35 of them passed whereas the other 15 failed. What is the probability that a student drawn at random passed the exam?

A.

0.15

B.

0.3

C.

0.35

D.

0.7

#### SOLUTION

Solution : D

Total number of students in a class = 50

Number of students who passed an examination = 35

Probability that a student passed the exam = Number of students who passed an examinatioTotal number of students in a class

Probability that a student passed the exam = 3550=0.7.

Two dice are thrown simultaneously.  Find the probability of getting a sum of 12.

A.

18

B.

19

C.

112

D.

136

#### SOLUTION

Solution : D

Total number of outcomes when two dice are thrown =
(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) = 36 .

Sum of 12 = (6,6)

Therefore, Probability of getting a sum of 12 = 136.

Which of the following can be the probability of an event?

A.

21/20

B.

-0.5

C.

3

D.

0.001

#### SOLUTION

Solution : D

The probability of an event always lies between 0 and 1 (0 and 1 inclusive).

Hence, among the options, only 0.001 can be the probability of an event.

A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table:

OutcomeFrequency116521753180415051456185

What is the probability of getting  2 or 4?

A.

0.515

B.

0.245

C.

0.325

D.

0.455

#### SOLUTION

Solution : C

Number of times  2 or 4 appears when a die was rolled = 175 + 150 = 325

Total number of times a die is thrown = 1000

Probability of getting a 2 or a 4 =number of times 2 or 4 appearstotal number of times a die is thrown

Probability=3251000=0.325

In a carton of 120 fruits, 24 are rotten. The probability that a fruit taken at random will be good is ___.

#### SOLUTION

Solution :

Number of good fruit = 120 – 24 = 96

Total number of fruits = 120

Probability of picking a good fruit =Number of good fruitTotal number of fruits

Probability of picking a good fruit =96120=0.8.

If a die is thrown 50 times and six appears 8 times, then the probability of getting a six is _______.

A.

0.16

B.

18

C.

850

D.

38

#### SOLUTION

Solution : A and C

A six appears on a die 8 times out of 50 times.

Number of times six appears on the die = 8

Number of times the die is thrown = 50

Probability of getting a six =number of times six appears on the dietotal number of times the die is thrown

Probability of getting a six =850=0.16

The probability of an event happening is 0.13, what will be the probability of the event not happening?

A. 0.87
B. 0.54
C. 0.23
D. 0.34

#### SOLUTION

Solution : A

There are always two possibilities with an event, either it will happen or it will not happen.

We know that the sum of probabilities of all possible outcomes of an event is 1.

The sum of probabilities of an event happening and an event not happening = 1

Let P(E) be the probability of an event happening.
(Then, P(not E) is the probability of the event not happening)

Then, P(E) = 0.13  (Given)

P(not E) = 1 – 0.13 = 0.87

The set of all possible outcomes associated with an experiment is called as________.

A. outcomes
B. sample space
C. trials
D. None of the above

#### SOLUTION

Solution : B

In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.

For example, if we toss a single coin then the chances are that either head will appear or tail will appear, the sample space will be {H}, {T}.