Question

Two events $X$ and $Y$ are occuring simultaneously. Probability of occurance of event $X$ is $0.64$ and that of event $Y$ when event $X$ has already occured is $0.32$. What will be the probability of occurance of events $X$ and $Y$ simultaneously?

• A. $0.2048$
• B. $0.2400$
• C. $0.6400$
• D. $0.3200$

Answer 1

The correct option is A $0.2048$

Given the probability of occurance of event $X$ is $\text{P(X)}=0.64$

And, probability of occurance of events $Y$ when $X$ has already occured is $\text{P(Y knowing X has already occured )}=0.32$

So, the probability of occurance of $X$ and $Y$ simultaneously is $\text{P(X and Y)}$
$\Rightarrow \text{P(X and Y)=P(X)}\times \text{P(Y knowing X has already occured)}$
$\Rightarrow \text{P(X and Y)}=0.64\times 0.32=0.2048$