Probability — Maths STD 12 Science — Question

4. 0.96

Solution:

We have,

P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6

As, P(B|A) = 0.6

$\Rightarrow\ \frac{\text{P}(\text{A}\cap\text{B})}{\text{P(A)}}=0.6$

$\Rightarrow\ \text{P}(\text{A}\cap\text{B})=0.6\times\text{P(A)}$

$\Rightarrow\ \text{P}(\text{A}\cap\text{B})=0.6\times0.4$

$\Rightarrow\ \text{P}(\text{A}\cap\text{B})=0.24$

Now, $\text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}-\text{P}(\text{A}\cap\text{B})$

$=0.4+0.8-0.24$

$=1.2-0.24$

$=0.96$

Hence, the correct alternative is option (d).