Question

Let A and B be two events such that P(A)=0.6, P(B) = 0.2 and P(A/B)=0.5. Then P (A'/B')
equals
(a) 1/10
(b) 3/10
(C) 3/8
(d) 6/7​

Answer 1

Answer:

option (C)  is correct

Step-by-step explanation:

Given:

$P(A)=0.6,\;\;P(B)=0.2\;\;P(\frac{A}{B})=0.5$

$P(\frac{A}{B})=0.5\implies\frac{P(A\cap\,B)}{P(B)}=0.5$

$\implies\frac{P(A\cap\,B)}{0.2}=0.5$

$\implies\bf\,P(A\cap\,B)=0.1$

Now,

By addition theorem of probability

$\boxed{\bf\,P(A\cup\,B)=P(A)+P(B)-P(A\cap\,B)}$

$P(A\cup\,B)=0.6+0.2-0.1$

$P(A\cup\,B)=0.7$

$P(\frac{A'}{B'})$

$=\frac{P(A'\cap\,B')}{P(B')}$

$=\frac{P((A\cup\,B)')}{P(B')}$

$=\frac{1-P(A\cup\,B)}{1-P(B)}$

$=\frac{1-0.7}{1-0.2}$

$=\frac{0.3}{0.8}$

$=\frac{3}{8}$

$\implies\boxed{\bf\,P(\frac{A'}{B'})=\frac{3}{8}}$

Answer 2

Answer:

3/8

Step-by-step explanation:

Refer photo for full solution.

Sorution not required for 1 Mark questions