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
