Question

Two events A and B are occuring simultaneously. Probability of occuring of event A is $0.4$ and probability of events A and B occuring together is $0.8$. What will be the probability of non - occurance of B event if replacement is allowed?

• A. $0.2$
• B. $0.8$
• C. $0.4$
• D. $1$

Answer 1

The correct option is B $0.8$

Given that replacement is possible,
$\Rightarrow$ this is an independent event.

So, $\text{P(A and B) = P(A)}\times \text{P(B)}$

Where, probability of occurance of event A be $\text{P(A)}$.

Probability of occurance of event B be $\text{P(B)}$.

And, probability of occurance of event A and B together be $\text{P(A and B)}$.

Also, $\text{P(A and B)}=0.8$

$\text{P(A)}=0.4$
$\Rightarrow 0.8=0.4\times \text{P(B)}$
$\Rightarrow \text{P(B)}=0.2$

Probability of occurance of event B will be $0.2$.

But we have to find probability of non occurance of event B
$\Rightarrow 1-\text{P(B)}=1-0.2=0.8$

So, the probability of non occurance of event B will be $0.8$.