Question

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

(i) P(A ∪ B) (ii) P(A ∩ B) (iii) P(A ∩ $\overline{B}$) (iv) P( $\overline{A}$ ∩ $\overline{B}$) [NCERT EXEMPLAR]

Answer 1

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

∴ P(A ∩ B) = 0

Also, P(A) = 0.35 and P(B) = 0.45.

(i)
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

= 0.35 + 0.45 − 0

= 0.80

(ii) A and B are mutually exclusive events.

∴ P(A ∩ B) = 0

(iii)
$$\begin{gathered} \mathrm{P}\left(A\cap \overline{B}\right)=\mathrm{P}\left(A\right)-\mathrm{P}\left(A\cap B\right) \\ =0.35-0 \\ =0.35 \end{gathered}$$

(iv)
$$\begin{gathered} \mathrm{P}\left(\overline{A}\cap \overline{B}\right)=\mathrm{P}\left(\overline{A\cup B}\right) \\ =1-\mathrm{P}\left(A\cup B\right) \\ =1-0.80 \\ =0.20 \end{gathered}$$