# Inter 2nd Year Maths 2A Probability Solutions Ex 9(a)

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.