# Data Handling

## Exercise 4.2

1). List the outcomes you can see in these experiments.

(a) Spinning a wheel (b) Tossing two coins together

Solution:

(a) Spinning a wheel

Possible outcomes = { A, B, C, D, E }

(b) Tossing two coins together

Possible outcomes = { HH, HT, TH, TT }

2). When a die is thrown, list the outcomes of an event of getting

(i) (a) a prime number (b) not a prime number.

Solution:

(a) a prime number

Possible outcomes = { 2, 3, 5 }

(b) not a prime number.

Possible outcomes = { 1, 4, 6 }

(ii) (a) a number greater than 5

Possible outcomes = { 6 }

(b) a number not greater than 5.

Possible outcomes = { 1, 2, 3, 4, 5 }

3). Find the.

(a) Probability of the pointer stopping on D in (Question 1-(a))?

(b) Probability of getting an ace from a well shuffled deck of 52 playing cards?

(c) Probability of getting a red apple. (See figure below)

Solution:

(a) Probability of the pointer stopping on D in (Question 1-(a))?

Possible outcomes = { A, B, C, D, E }

n(S)= 5

Let A be the event of the pointer stopping on D.

Expected outcome = D

n(A)= 1

p(A)= ^{n(A)}/_{n(S)}

= ^{1}/_{5}

(b) Probability of getting an ace from a well-shuffled deck of 52 playing cards?

Possible outcomes = 52

n(S)= 52

Let A be the event the card is an ace

Expected outcome = Ace card

n(A)= 4

p(A)= ^{n(A)}/_{n(S)}

= ^{4}/_{52}

= ^{1}/_{13}

(c) Probability of getting a red apple. (See figure below)

Possible outcomes = { G, R, R, R, G, R, G }

n(S)= 7

Let A be the event of getting a red apple.

Expected outcome = Red apple = { R, R, R, R }

n(A)= 4

p(A)= ^{n(A)}/_{n(S)}

= ^{4}/_{7}

4). Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of.

(i) getting a number 6?

(ii) getting a number less than 6?

(iii) getting a number greater than 6?

(iv) getting a 1-digit number?

Solution:

Possible outcomes = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

n(S) = 10

(i) getting a number 6?

Let A be the event of getting number 6

Expected outcome = { 6 }

n(A) = 1

p(A)= ^{n(A)}/_{n(S)}

= ^{1}/_{10}

(ii) getting a number less than 6?

Let B be the event of getting number less than 6

Expected outcome = { 1, 2, 3, 4, 5 }

n(B) = 5

p(B)= ^{n(B)}/_{n(S)}

= ^{5}/_{10}

= ^{1}/_{2}

(iii) getting a number greater than 6?

Let C be the event of getting number greater than 6

Expected outcome = { 7, 8, 9, 10 }

n(C) = 4

p(C)= ^{n(C)}/_{n(S)}

= ^{4}/_{10}

_{ }= ^{2}/_{5}

(iv) getting a 1-digit number?

Let D be the event of getting a 1-digit number

Expected outcome = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }

n(D) = 9

p(D)= ^{n(D)}/_{n(S)}

= ^{9}/_{10}

5). If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non blue sector?

Possible outcomes = { G, G, G, B, R }

n(S) = 5

let A be the event of getting a green sector

Expected outcomes = { G, G, G }

n(A) = 3

p(A)= ^{n(A)}/_{n(S)}

= ^{3}/_{5}

Let B be the event of getting a non blue sector

Expected outcome = { G, G, G, R }

n(B) = 4

p(B)= ^{n(B)}/_{n(S)}

= ^{4}/_{5}

6). Find the probabilities of the events given in Question 2.

Possible outcomes = { 1, 2, 3, 4, 5, 6 }

n(S) = 6

(a) a prime number

Let A be the event of getting a prime number

Possible outcomes = { 2, 3, 5 }

n(A) = 3

p(A)= ^{n(A)}/_{n(S)}

= ^{3}/_{6}

_{ }= ^{1}/_{2}

(b) not a prime number.

Let B be the event of getting not a prime number

Possible outcomes = { 1, 4, 6 }

n(A) = 3

p(A)= ^{n(A)}/_{n(S)}

= ^{3}/_{6}

_{ }= ^{1}/_{2}

(ii) (a) a number greater than 5

Let C be the event of getting number greater than 5

Expected outcome = { 6 }

n(C) = 1

p(C)= ^{n(C)}/_{n(S)}

= ^{1}/_{6}_{ }

(b) a number not greater than 5.

Let D be the event of getting a number not greater than 5

Expected outcome = { 1, 2, 3, 4, 5 }

n(D) = 5

p(D)= ^{n(D)}/_{n(S)}

= ^{5}/_{6}

Click here for the solutions of Std 8 Maths

1). Rational Numbers

2). Linear Equations in One Variable

3). Understanding Quadrilaterals

4). Data Handling