Question

two events, x and y, are independent of each other. p(y) = 1/8 and p(x and y)=1/4. what is p(x) written as a decimal? round to the nearest tenth, if necessary.

Explanation:

Step1: Recall independence formula

For independent events $X$ and $Y$, $P(X\cap Y)=P(X)\times P(Y)$.

Step2: Rearrange formula to find $P(X)$

Given $P(Y)=\frac{1}{8}$ and $P(X\cap Y)=\frac{1}{16}$, we have $P(X)=\frac{P(X\cap Y)}{P(Y)}$.

Step3: Substitute values

$P(X)=\frac{\frac{1}{16}}{\frac{1}{8}}=\frac{1}{16}\times\frac{8}{1}=\frac{1}{2} = 0.5$

Answer:

0.5