Question

Let $A$ and $B$be events for which $P\left(A\right)=x$, $P\left(B\right)=y$, $P(A\cap B)=z$ then $P(A\text{'}\cap B)$ equals

• A. $\left(1-x\right)y$
• B. $1-x+y$
• C. $y-z$
• D. $1-x+y-x$

Answer 1

The correct option is C

$y-z$

Explanation for correct answer:

Finding $P(A\text{'}\cap B)$:

Given,

$P\left(A\right)=x$, $P\left(B\right)=y$, $P(A\cap B)=z$

Finding $P(A\text{'}\cap B)$

We know that

$$\begin{gathered} P\left(A\text{'}\cap B\right)=P\left(B\right)-P\left(A\cap B\right) \\ =y-z \end{gathered}$$

Hence, the correct answer is option (C)