Exercise 4.2

Q1

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

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

Sol

Solution:

(a) From the given figure, we can see that a total of letters are on a spinning wheel i.e. , B , and . So, there are a total of possible outcomes.

(b) When two coins are tossed together, we will have a total of possible outcomes.

These outcomes are as follows: HHH, HTT, THH and TTT.

Q2

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

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

(ii) (a) a number greater than 5 (b) a number not greater than 5.

Sol

Solution:

(i)

(a) The outcomes for the event of "getting a prime number" are , and . (Enter the values in ascending)

(b) The outcomes of the event of "not getting a prime number" are , and . (Enter the values in ascending)

(ii)

(a) The outcomes of the event of "getting a number greater than 5" is .

(b) The outcomes of the event of "not getting a number greater than 5" are , , , and .

Q3

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)

Sol

Solution:

(a) In the given spinning wheel: there are pointers

The possible outcomes are , , , , . (Enter the letters in order)

So, there are outcomes. The pointer stops at D, which is outcome.

Thus, the probability of "the pointer landing on the letter D" =

(b) There are aces in a deck of playing cards. So, there are events for getting an ace.

So, the probability of "getting an ace" = 4524852 =

(c) Total number of apples =

Number of red apples =

Probability of getting a red apple =

Q4

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?

Sol

Solution:

(i) Outcome of getting a number 6 from ten slips is .

Thus, the probability of "getting the number 6" =

(ii) Numbers less than 6 are , , , and . So, there are a total of outcomes.

Thus, the probability of "getting a number less than 6" = 510410 =

(iii) Number greater than 6 out of ten are , , , . So, there are a total of possible outcomes.

Thus, the probability of "getting a number greater than 6" = 410610 =

(iv) The one-digit numbers in the possible outcomes are , , , , , , , , .

Thus, the probability of "getting a 1-digit number" =

Q5

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?

Sol

Solution:

A total of sectors are present.

Out of the five sectors, sectors are green.

Therefore, probability of "getting a green sector" =

Out of the five sectors, sector is blue. Hence, non-blue sectors = – = sectors

Hence, probability of "getting a non-blue sector" =

Q6

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

Sol

Solution:

When a die is thrown, there is a total of six outcomes, i.e., , , , , and .

(i) (a) getting a prime number

, , are the prime numbers. So, there are outcomes out of .

Hence, probability of "getting a prime number" = 3646 =

(b) getting not a prime number

, , are not the prime numbers. So, there are outcomes out of .

Hence, probability of "not getting a prime number" = 3646 =

(ii) (c) number greater than 5

Only is greater than 5.

So there is outcome out of 6.

Hence, probability of "getting a number greater than 5" =

(d) number not greater than 5

Numbers not greater than 5 are , , , and .

So there are outcomes out of 6.

Hence, probability of "not getting a number greater than 5" =