Practicing the Intermediate 2nd Year Maths 2A Textbook Solutions Inter 2nd Year Maths 2A Probability Solutions Exercise 9(a) will help students to clear their doubts quickly.

## Intermediate 2nd Year Maths 2A Probability Solutions Exercise 9(a)

I. In the experiment of throwing a die, consider the following events:

Question 1.

A = {1, 3, 5}, B = {2, 4, 6}, C = {1, 2, 3} Are these events equally likely?

Solution:

Since events A, B, C has an equal chance to occur, hence they are equally likely events.

Question 2.

In the experiment of throwing a die, consider the following events:

A = {1, 3, 5}, B = {2, 4}, C = {6}

Are these events mutually exclusive?

Solution:

Since the happening of one of the given events A, B, C prevents the happening of the other two, hence the given events are mutually exclusive.

Otherwise A ∩ B = φ, B ∩ C = φ, C ∩ A = φ

Hence they are mutually exclusive events.

Question 3.

In the experiment of throwing a die, consider the events.

A = (2, 4, 6}, B = {3, 6}, C = {1, 5, 6}

Are these events exhaustive?

Solution:

A = {2, 4, 6}, B = {3, 6}, C = {1, 5, 6}

Let S be the sample space for the random experiment of throwing a die

Then S = {1, 2, 3, 4, 5, 6}

∵ A ⊂ S, B ⊂ S and C ⊂ S, and A ∪ B ∪ C = S

Hence events A, B, C are exhaustive events.

II.

Question 1.

Give two examples of mutually exclusive and exhaustive events.

Solution:

Examples of mutually exclusive events:

(i) The events {1, 2}, {3, 5} are disjoint in the sample space S = {1, 2, 3, 4, 5, 6}

(ii) When two dice are thrown, the probability of getting the sums of 10 or 11.

Examples of exhaustive events:

(i) The events {1, 2, 3, 5}, (2, 4, 6} are exhaustive in the sample space S = {1, 2, 3, 4, 5, 6}

(ii) The events {HH, HT}, {TH, TT} are exhaustive in the sample space S = {HH, HT, TH, TT} [∵ tossing two coins]

Question 2.

Give examples of two events that are neither mutually exclusive nor exhaustive.

Solution:

(i) Let A be the event of getting an even prime number when tossing a die and let B be the event of getting even number.

∴ A, B are neither mutually exclusive nor exhaustive.

(ii) Let A be the event of getting one head tossing two coins.

Let B be the event of getting atleast one head tossing two coins.

∴ A, B are neither mutually exclusive nor exhaustive.

Question 3.

Give two examples of events that are neither equally likely nor exhaustive.

Solution:

(i) Two coins are tossed

Let A be the event of getting an one tail and

Let B be the event of getting atleast one tail.

∴ A, B are neither equally likely nor exhaustive.

(ii) When a die is tossed

Let A be the event of getting an odd prime number and

Let B be the event of getting odd number.

∴ B are are neither equally likely nor exhaustive.