If P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6 then P(A )= - Vidyadip

MCQ

If $P(A) = 0.4, P(B) = 0.8$ and $P(B|A) = 0.6$ then $\text{P}(\text{A}\cup\text{B})=$

A
$0.24$
B
$0.3$
C
$0.48$
✓
$0.96$

✓

Answer

Correct option: D.

$0.96$

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 $(d).$

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