Given: A and B are two mutually exclusive events.

P (A) = 0.4 and P (B) = 0.5

By definition of mutually exclusive events we know that:

P (A ∪ B) = P (A) + P (B)

Now, we have to find

**(i)** P (A ∪ B) = P (A) + P (B) = 0.5 + 0.4 = 0.9

**(ii)** P (A′ ∩ B′) = P (A ∪ B)′ {using De Morgan’s Law}

P (A′ ∩ B′) = 1 – P (A ∪ B)

= 1 – 0.9

= 0.1

**(iii)** P (A′ ∩ B) [This indicates only the part which is common with B and not A.

Hence this indicates only B]

P (only B) = P (B) – P (A ∩ B)

As A and B are mutually exclusive so they don’t have any common parts.

P (A ∩ B) = 0

∴ P (A′ ∩ B) = P (B) = 0.5

**(iv)** P (A ∩ B′) [This indicates only the part which is common with A and not B.

Hence this indicates only A]

P (only A) = P (A) – P (A ∩ B)

As A and B are mutually exclusive so they don’t have any common parts.

P (A ∩ B) = 0

∴ P (A ∩ B′) = P (A) = 0.4

Answered by Sakshi | 1 year agoOne 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 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 die is thrown twice. What is the probability that at least one of the two throws come up with the number 3?

A natural number is chosen at random from amongst first 500. What is the probability that the number so chosen is divisible by 3 or 5?