Question

If p(not a) =0.7 , p(b)=0.7 and p(b/a) =0.5 find p(a/b)

Answer 1

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Answer 2

The value is $p(a/b)=\frac{3}{14}$

Step-by-step explanation:

Given : If p(not a)=0.7, p(b)=0.7 and p(b/a) =0.5

To find : The value of p(a/b) ?

Solution :

We have given,

$p(\text{not a})=0.7$

$p(a)=1-p(\text{not a})$

$p(a)=1-0.7$

$p(a)=0.3$

Now, $p(b/a)=\frac{p(a\cap b)}{p(a)}$

Substitute the value,

$0.5=\frac{p(a\cap b)}{0.3}$

$p(a\cap b)=0.5\times 0.3$

$p(a\cap b)=0.15$

So, $p(a/b)=\frac{p(a\cap b)}{p(b)}$

$p(a/b)=\frac{0.15}{0.7}$

$p(a/b)=\frac{3}{14}$

Therefore, the value is $p(a/b)=\frac{3}{14}$

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