two events, x and y, are independent of each other. $p(y)=\frac{5}{6}$ and $p(x \text{ and }…

two events, x and y, are independent of each other. $p(y)=\frac{5}{6}$ and $p(x \text{ and } y)=\frac{1}{3}$. what is $p(x)$ written as a decimal? round to the nearest tenth, if necessary.\n0.2\n0.3\n0.4\n0.5

two events, x and y, are independent of each other. $p(y)=\frac{5}{6}$ and $p(x \text{ and } y)=\frac{1}{3}$. what is $p(x)$ written as a decimal? round to the nearest tenth, if necessary.\n0.2\n0.3\n0.4\n0.5

Answer

Explanation:

Step1: Recall the formula for independent events

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

Step2: Rearrange the formula to solve for $P(X)$

$P(X)=\frac{P(X\cap Y)}{P(Y)}$.

Step3: Substitute the given values

Given $P(Y)=\frac{5}{6}$ and $P(X\cap Y)=\frac{1}{3}$, then $P(X)=\frac{\frac{1}{3}}{\frac{5}{6}}$.

Step4: Simplify the fraction

$P(X)=\frac{1}{3}\times\frac{6}{5}=\frac{6}{15} = 0.4$.

Answer:

C. 0.4