These AP 9th Class Maths Important Questions 14th Lesson Probability will help students prepare well for the exams.

## AP State Syllabus 9th Class Maths 14th Lesson Important Questions and Answers Probability

Question 1.

Find out the probability of picking a number which is a prime number randomly from 20 to 30 (Including) natural numbers.

Solution:

No. of prime numbers between 20 and 30 = 23, 29

Total numbers = 10

Probability = \(\frac{2}{10}=\frac{1}{5}\)

Question 2.

By picking a natural number randomly upto 100, find the probability of the number being a perfect cube.

Solution:

Probability of the number being a perfeet cube by picking a natural number randomly upto 100.

⇒ P(E) = \(\frac{\text { favourable outcomes }}{\text { total outcomes }}\)

= \(\frac{4}{100}=\frac{1}{25}\)

Question 3.

If a dice with six faced rolled randomly find.

i) The probability of getting an even number on the top face.

ii) The probability of getting a prime number on the top face.

iii) The probability of getting 7 on the top face

iv) The probability of getting a number on the top face which have the sum of the factors of that number is twice to that number. (Which is called as a perfect number)

Solution:

When die was rolled possible outcomes are 1, 2, 3, 4, 5, 6

Total outcomes = 6

i) Even numbers in outcomes = 2, 4, 6 = 3

∴ Required probability = \(\frac{4}{6}=\frac{2}{3}\)

ii) Prime numbers = 1, 2, 3, 5 = 4

∴ Required probability = \(\frac{4}{6}=\frac{2}{3}\)

iii) Getting ‘7’ on top = 0

∴ This is impossible event.

iv) Sum of the factors of that number is twice to that numbers = 6

∴ Required probability = \(\frac{1}{6}\)

Question 4.

A letter is chosen from English alphabet. Find the probability of the letter choosen is

i) a consonant

ii) both consonant and vowel

iii) a letter comes before M

iv) not a vowel

Solution:

Favourable outcomes = 26

i) Vowels

Favourable outcomes = 21

∴ Probability = \(\frac{21}{26}\)

ii) Vowel and Consonants Favourable outcomes = 0

∴ Probability = \(\frac{0}{26}\) = 0

iii) A letter comes before M Favourable outcomes =12

∴ Probability = \(\frac{12}{26}=\frac{6}{13}\)

iv) Not a vowel Favourable outcomes = 21

∴ Probability = \(\frac{21}{26}\)

Choose the correct answer:

Question 1.

Getting a ‘head’ when an unbiased coin is tossed is …………………

A) less likely

B) equally likely

C) more likely

D) certain

Answer:

B) equally likely

Question 2.

When a die is thrown, getting a number more than 6 is

A) less likely

B) equally likely

C) more likely

D) impossible

Answer:

D) impossible

Question 3.

The number of possible outcomes when a die is thrown is

A) 1

B) 4

C) 6

D) 4

Answer:

C) 6

Question 4.

When two dice are thrown, the total outcomes are

A) 12

B) 6

C) 1

D) 36

Answer:

D) 36

Question 5.

When a coin is tossed, the total possible outcomes are

A) 1

B) 2

C) 3

D) 4

Answer:

B) 2

Question 6.

The experiment in which all possible outcomes are known but exact outcome can’t be predicted is called

A) Mathematical experiment

B) Trial

C) Even

D) Outcome

Answer:

B) Trial

Question 7.

The each outcome of a random experiment is called

A) event

B) trial

C) chance

D) none

Answer:

A) event

Question 8.

The probability of getting a head when a coin is tossed is

A) 1

B) \(\frac{1}{4}\)

C) \(\frac{1}{2}\)

D) \(\frac{1}{8}\)

Answer:

C) \(\frac{1}{2}\)

Question 9.

If two identical coins are tossed, the probability of getting two heads is

A) \(\frac{1}{2}\)

B) \(\frac{1}{4}\)

C) \(\frac{1}{6}\)

D) \(\frac{1}{8}\)

Answer:

B) \(\frac{1}{4}\)

Question 10.

The probability of getting atmost two heads when three coins are tossed is

A) \(\frac{1}{8}\)

B) 8

C) \(\frac{7}{8}\)

D) \(\frac{3}{8}\)

Answer:

C) \(\frac{7}{8}\)

Question 11.

If two coins are tossed, the chance of getting np heads is

A) \(\frac{3}{4}\)

B) \(\frac{1}{4}\)

C) \(\frac{1}{2}\)

D) None

Answer:

B) \(\frac{1}{4}\)

Question 12,

Sum of the probabilities of getting a head and a tail when an unbiased coin is tossed is

A) \(\frac{1}{2}\)

B) \(\frac{1}{4}\)

C) 1

D) 0

Answer:

C) 1

Question 13.

Sum of probabilities of getting an even number and an odd number when a die is rolled is

A) \(\frac{1}{2}\)

B) \(\frac{1}{6}\)

C) \(\frac{1}{3}\)

D) 1

Answer:

D) 1

Question 14.

The sum of the probabilities of all outcomes of a Random experiment is always

A) 0

B) – 1

C) 1

D) \(\frac{1}{2}\)

Answer:

C) 1

Question 15.

The probability of an event which is certain

A) 0

B) 1

C) -1

D) Can’tsay

Answer:

B) 1

Question 16.

The probability of an event which is impossible

A) 0

B) -1

C) 1

D) 2

Answer:

A) 0

Question 17.

The probability of an event always lie between

A) 1 and 2

B) -1 and 1

C) -1 and 0

D) 0 and 1

Answer:

D) 0 and 1

Question 18.

The probability of drawing a prime number from a pack of cards numbered from 1 to 10

A) \(\frac{2}{10}\)

B) \(\frac{1}{10}\)

C) \(\frac{5}{10}\)

D) \(\frac{2}{5}\)

Answer:

D) \(\frac{2}{5}\)

Question 19.

The probability of “the last day of a month is Sunday”

A) \(\frac{2}{7}\)

B) \(\frac{1}{7}\)

C) \(\frac{3}{7}\)

D) \(\frac{4}{7}\)

Answer:

B) \(\frac{1}{7}\)

Question 20.

When a die is thrown, equally likely events are getting

A) even number and odd number

B) prime and composite

C) multiple of 3 and multiple of 2

D) numbers less than 3 and numbers greater than 3

Answer:

A) even number and odd number

Question 21.

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

A) 0.9

B) – 1.5

C) 10%

D) 2/5

Answer:

B) – 1.5

Question 22.

A letter is chosen at random from the word “ROSE”. Find the probability, that the letter chosen is a vowel.

A) \(\frac{1}{4}\)

B) \(\frac{3}{4}\)

C) \(\frac{1}{2}\)

D) \(\frac{2}{5}\)

Answer:

C) \(\frac{1}{2}\)

Question 23.

Two coins are tossed simultaneously. What is the number of all outcomes?

A) 3

B) 4

C) 2

D) 1

Answer:

B) 4

Question 24.

Three coins are tossed simultaneously. What is the number of all possible outcomes?

A) 8

B) 6

C) 4

D) 2

Answer:

A) 8

Question 25.

The probability winning a prize is

A) 0

B) \(\frac{1}{2}\)

C) 2

D) 1

Answer:

B) \(\frac{1}{2}\)

Question 26.

If probability of a certain event A is P(A) = x, then P’(A) is

A) \(\frac{1}{\mathrm{x}}\) – 1

B) 1 – \(\frac{1}{\mathrm{x}}\)

C) \(\frac{1}{\mathrm{x}}\)

D) 1 – x

Answer:

D) 1 – x

Question 27.

A die is thrown once. Find the probability of getting a number less than 3.

A) \(\frac{1}{2}\)

B) \(\frac{1}{3}\)

C) \(\frac{1}{4}\)

D) \(\frac{1}{6}\)

Answer:

B) \(\frac{1}{3}\)

Question 28.

Which of the following is true?

A) 0 ≤ P(A) ≤ 1

B) P(A) > 1

C) P(A) < 0

D) -1 ≤ P(A) ≤ 1

Answer:

A) 0 ≤ P(A) ≤ 1

Question 29.

Probability of picking a two-digited number radomly for which the units and ten’s places have same digits

A) 1/10

B) 9/10

C) 9/100

D) 1/100

Answer:

A) 1/10

Question 30.

Which of the following is not to be a probability of any event ?

A) 0

B) 1

C) – 0.2

D) 0.75

Answer:

C) – 0.2

Question 31.

Which of the following is an example for impossible event?

i) Getting 7 on the top when a dice is rolled

ii) Getting head on the top while tossing a coin

iii) Picking a spade from a deck of playing cards

iv) Picking an even prime number less than 2

A) Both (i) & (ii)

B) Both (i) & (iii)

C) Both (i) & (iv)

D) Both (ii) & (iii)

Answer:

C) Both (i) & (iv)

Question 32.

In an exit poll for assembly elections winning of a person is 50%. Then the probability of his loosing is

A) 25%

B) 75%

C) 100%

D) 50%

Answer:

D) 50%

Question 33.

When a dice is rolled, total number of possible outcomes are

A) 4

B) 5

C) 7

D) 6

Answer:

D) 6

Question 34.

While tossing a coin the probability of getting head on upper side is

A) 1/4

B) 1/2

C) 1/3

D) 3/4

Answer:

B) 1/2

Question 35.

If the probability of an event is 1, then the event is called as

A) Equal likely event

B) Impossible event

C) Certain event

D) Mutually exclusive event

Answer:

A) Equal likely event

Question 36.

When a six faced dice is rolled the probability that the top face number is a perfect square and also a perfect cube is

A) 1/6

B) 1/4

C) 1/3

D) 2/3

Answer:

C) 1/3

Question 37.

The probability that random selected month to have 32 days

A) 0

B) \(\frac{32}{365}\)

C) \(\frac{1}{32}\)

D) 1

Answer:

A) 0

Question 38.

There are 5 balls iii a vessel. Out of which 2 are red, 2 are blue and ‘1’ is green. When a ball is selected at random, then probability that the ball is not a red ball …………………

A) 1/5

B) 2/5

C) 3/5

D) 4/5

Answer:

C) 3/5

Question 39.

The modal letter of the letters of the word “ASSESSMENTS”

A) A

B) E

C) S

D) T

Answer:

C) S

Question 40.

Probability of an event is P. Then ‘which of the following is TRUE ?

niafcj-r PI

A) 0 < P < 1 B) 0 > P > 1

C) 0 ≥ P ≥ 1

D) 0 ≤ P ≤ 1

Answer:

D) 0 ≤ P ≤ 1

Question 41.

In the formula P(E) = \(\frac{32}{365}\)

\(\frac{\mathbf{n}(\mathrm{E})}{\mathbf{n}(\mathrm{S})}\) ; n(E)

represents

A) No. of favourable outcomes

B) No. of not favourable outcomes

C) Total no. of outcomes

D) Probability of event

Answer:

A) No. of favourable outcomes