# Probability

## Exercise 5.3

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

(a) Spinning a wheel

**Answer** The List of Events is as follows: A, B, C, D

(b) Tossing two coins together

**Answer:** There will be following combinations of Head and Tail if two coins are tossed together:

HH, HT, TH, TT

Question 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.

**Answer:** List of events when a die is thrown:

1, 2, 3, 4, 5, 6

(i) List of Prime Numbers: 2, 3, 5

(ii) List of Non-prime numbers: 1, 4, 6

(iii) List of Number >5: 6

(iv) List of Number Not greater than 5: 1, 2, 3, 4, 5

Question 3: Find the.

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

**Answer:** Total number of events = 5

No. of favourable outcome = 1

So, probability of favourable outcome = 1/5

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

**Answer:** Total Number of events = 52

Number of Favourable outcomes = 4 (because there are 4 aces in a pack of cards)

Probability of favourable outcome = `4/(52) = 1/(13)`

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

**Answer:** Total number of events = 7

Number of Favourable outcomes = 4

Probability of favourable outcomes = `4/7`

Question 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?

**Answer:** Total number of events = 10

Number of favourable events for getting number 6 = 1

Probability of getting number `6=(1)/(10)`

Number of favorable outcomes for getting number less than 6 = 5

Probability of getting a number less than 6

`=(5)/(10)=1/2`

Probability of getting a number greater than 6

`=(4)/(10)=2/5`

Probability of getting a 1 digit number `=(9)/(10)`

Question 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?

**Answer:** Total number of events = 5

Probability of getting green `=3/5`

Probability of getting blue `=1/5`

So, probability of getting non-blue `=1-1/5=(5-1)/(5)=4/5`

Question 6: Find the probabilities of the events given in Question

Probability of getting prime numbers `=3/6=1/2`

Probability of getting non-prime numbers `=3/6=1/2`

Probability of getting a number greater than 5 `=1/6`

Probability of getting a number not greater than 5 `=5/6`