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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 9 Probability Ex 9.1

Question 1.

You are walking along a street. If you just choose a stranger crossing you, what is the probability that his next birthday will fall on a Sunday?

Solution:

Days in a week (S) = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

n( S) = 7

∴ No. of days in week = 7

Event of selecting Sunday (A) = {Sunday}

n(A) = 1

∴ Probability of selecting Sunday = \(\frac{n(\mathrm{A})}{n(\mathrm{S})}=\frac{1}{7}\)

Question 2.

What is the probability of drawing a King or a Queen or a Jack from a deck of cards?

Solution:

Number of cards n(S) = 52

No. of King cards n(A) = 4

No. of Queen cards n(B) = 4

No. of Jack cards n(C) = 4

Probability of drawing a King card

\(=\quad \frac{n(\mathrm{A})}{n(\mathrm{S})}=\frac{4}{52}\)

Probability of drawing a Queen card

\(=\frac{n(\mathrm{B})}{n(\mathrm{S})}=\frac{4}{52}\)

Probability of drawing a Jack card

\(=\frac{n(\mathrm{C})}{n(\mathrm{S})}=\frac{4}{52}\)

The Probability of drawing a King or a Queen or a Jack from a deck of cards

\(=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})+\mathrm{P}(\mathrm{C})=\frac{4}{52}+\frac{4}{52}+\frac{4}{52}=\frac{4+4+4}{52}=\frac{12}{52}=\frac{3}{13}\)

Question 3.

What is the probability of throwing an even number with a single standard dice of six faces?

Solution:

Faces of a dice (S) = {1, 2, 3, 4, 5, 6}

n(S) = 6

Event of throwing an even number

A = {2, 4, 6}, n(A) = 3

Question 4.

There are 24 balls in a pot. If 3 of them are Red, 5 of them are Blue and the remaining are Green then, what is the probability of picking out

(i) a Blue ball,

(ii) a Red ball and

(iii) a Green ball?

Solution:

n(S) = 24

Red – n(R) = 3

Blue – n(B) = 5

Green – n(G) = 16

Question 5.

When two coins are tossed, what is the probability that two heads are obtained?

Solution:

Sample space when two coins are tossed (S) = {HH, TT, HT, TH}

n(S) = 4

Event of getting two heads (A) = {HH}

n(A) = 1

Probability of getting two heads P(A) = \(\frac{n(\mathrm{A})}{n(\mathrm{S})}=\frac{1}{4}\)

Question 6.

Two dice are rolled, find the probability that the sum is

(i) equal to 1

(ii) equal to 4

(iii) less than 13

Solution:

When two dice are rolled Sample space

Question 7.

A manufacturer tested 7000 LED lights at random and found that 25 of them were defective. If a LED light is selected at random, what is the probability that the selected LED light is a defective one.

Solution:

n(S) = 7000 S – Total no. of lights.

n(A) = 25 A – Defective ones.

Question 8.

In a football match, a goalkeeper of a team can stop the goal, 32 times out of 40 attempts tried by a team. Find the probability that the opponent team can convert the attempt into a goal.

Solution:

Total no. of attempts n(S) = 40

Total no. of attempts by A team n(A) = 32

Total no. of attempts by the opponent team B = n(B) = 40 – 32 = 8

Question 9.

What is the probability that the spinner will not land on a multiple of 3?

Solution:

Total no. of choices n(S) = 8

Total no. of multiples of 3 A = {3, 6}

n(A) = 2

Event of non-multiples of 3B = {1, 2, 4, 5, 7, 8}

n(B) = 6

Question 10.

Frame two problems in calculating probability, based on the spinner shown here.

Solution:

(i) What is the probability that the spinner will land on an even number?

(ii) What is the probability that the spinner will not land on a prime number.