# 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

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