**Question:**

**If A and B are mutually exclusive events, P (A) = 0.35 and P (B) = 0.45, find**

**(a) P (A′)**

**(b) P (B′)**

**(c) P (A ∪ B)**

**(d) P (A ∩ B)**

**(e) P (A ∩ B′)**

**(f) P (A′∩ B′)**

**Solution:**

Given that P (A) = 0.35 and P (B) = 0.45

∵ The events A and B are mutually exclusive then P (A ⋂ B) = 0

(a) To find (a) P (A′)

We know that,

P (A) + P (A’) = 1

⇒ 0.35 + P(A’) = 1 [given]

⇒ P (A’) = 1 – 0.35

⇒ P (A’) = 0.65

(b) To find (b) P (B′)

We know that,

P (B) + P (B’) = 1

⇒ 0.45 + P (B’) = 1

⇒ P (B’) = 1 – 0.45

⇒ P (B’) = 0.55

(c) To find (c) P (A ⋃ B)

We know that,

P (A ∪ B) = P (A) + P (B) – P (A ∩ B)

⇒ P (A ⋃ B) = 0.35 + 0.45 – 0 [given]

⇒ P (A ⋃ B) = 0.80

(d) To find (d) P (A ⋂ B)

It is given that A and B are mutually exclusive events.

∴ P (A ⋂ B) = 0

(e) To find (e) P (A ⋂ B’)

P (A ⋂ B’) = P (A) – P (A ⋂ B)

= 0.35 – 0

= 0.35

(f) To find (f) P (A’ ⋂ B’)

P (A’ ⋂ B’) = P (A ⋃ B)’

= 1 – P (A ⋃ B)

= 1 – 0.8 [from part (c)]

= 0.2

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