Students must practice this TS Intermediate Maths 2A Solutions Chapter 9 Probability Ex 9(a) to find a better approach to solving the problems.
TS Inter 2nd Year Maths 2A Solutions Chapter 9 Probability Ex 9(a)
I.
Question 1.
In the experiment of throwing a die, consider the following events A = {1, 3, 5}, B = {2, 4, 6}, C = {1, 2, 3}. Are these events equally likely?
Solution:
If the die is thrown there is a possibility of getting 1 or 2 or 3 or 4 or 5 or 6 on any face.
Hence the events A = {1, 3, 5}, B = {2, 4, 6} and C = {1, 2, 3} are equiprobable since there is no reason to expect one in preference to others.
Hence the events A, B, C are equally likely.
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:
The three events A, B, C are mutually exclusive since the occurrence of one of the events prevents the happening of any one of the remaining events.
Since A ∩ B ∩ C = {1, 3, 5} ∩ {2, 4} ∩ {6}
We say that the events are A, B, C are mutually exclusive.
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:
The three events A, B, C are exhaustive if A ∪ B ∪ C = S
A ∪ B ∪ C = {2, 4, 6} ∪ {3, 6} ∪ {15 6}
= {1, 2, 3, 4, 5, 6} = S.
II.
Question 1.
Give two examples of mutually exclusive and exhaustive events.
Solution:
In tossing a coin there are two exhaustive events Head (H) and Tail (T).
In throwing a die there are six exhaustive events of getting I or 2 or 3 or 4 or 5 or 6.
In tossing a coin either heads comes up or tail but both cannot happen at the same time. These two events are mutually exclusive because happening of one event prevents the happening of the other.
In a well shuffled pack of cards if a card is drawn from 52 cards then getting an ace and getting a king are mutually exclusive events.
Question 2.
Give examples of two events that are neither mutually exclusive nor exhaustive.
Solution:
If a coin is tossed twice or two coins are tossed a time, then the events of getting head or tail are not mutually exclusive nor exhaustive.
Since we get {HH, HT, TH, TT} as events.
From a well shuffled pack of cards if two cards are drawn one after other with replacement, then getting aces on two attempts are not mutually exclusive nor exhaustive.
Question 3.
Give two examples of events that are neither equally likely nor exhaustive.
Solution:
If a die is thrown then the event of getting ‘1’ and the event of getting a prime number are neither equally likely events nor exhaustive events.
In the experiment of throwing a pair of dice then the events
E1 = A sum 7 ( of the numbers that appear on the uppermost faces of the dice ) and
E3 = A sum > 7 ( of the number that appear on the uppermost faces of the dice ) are neither equally likely nor mutually exclusive.