(i) A and B are mutually exclusive

(ii) A and B are mutually exclusive and exhaustive

(iii) A = BI

(iv) A and C are mutually exclusive

(v) A and BI are mutually exclusive.

(vi) AI, BI, C are mutually exclusive and exhaustive.

Asked by Abhisek | 1 year ago |  126

##### Solution :- (i) A and B are mutually exclusive

So, (A ∩ B) = φ

So, A & B are mutually exclusive.

Hence, the given statement is true.

(ii) A and B are mutually exclusive and exhaustive

A ∩ B = f and A ∪ B = S

Thus, the given statement is true.

(iii) It is observed that Thus, the given statement is true.

(iv) It is observed that A ∩ C = {(2, 1), (2, 2), (2, 3), (4, 1)} ≠ φ

A and C are not mutually exclusive.

Thus, the given statement is false.

(v)  A ∩ BI = A ∩ A = A

∴ A ∩ BI ≠ φ

A and B’ are not mutually exclusive

(vi) It is observed that A' ∪ B' ∪ C = S

However, Therefore, events A’, B’ and C are not mutually exclusive and exhaustive.

Thus, the given statement is false.

Answered by Pragya Singh | 1 year ago

### Related Questions

#### One number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6?

One number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6?

#### The probability that a student will pass the final examination in both English and Hindi is 0.5

The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75. What is the probability of passing the Hindi examination?

#### A card is drawn from a deck of 52 cards. Find the probability of getting an ace or a spade card.

A card is drawn from a deck of 52 cards. Find the probability of getting an ace or a spade card.