two events, a and b, are independent of each other. $p(a)=\frac{1}{6}$ and $p(a \text{ and }…

two events, a and b, are independent of each other. $p(a)=\frac{1}{6}$ and $p(a \text{ and } b)=\frac{1}{8}$. what is $p(b)$ written as a decimal? round to the nearest hundredth, if necessary.\n0.02\n0.04\n0.29\n0.75

two events, a and b, are independent of each other. $p(a)=\frac{1}{6}$ and $p(a \text{ and } b)=\frac{1}{8}$. what is $p(b)$ written as a decimal? round to the nearest hundredth, if necessary.\n0.02\n0.04\n0.29\n0.75

Answer

Explanation:

Step1: Recall the formula for independent events

For independent events $A$ and $B$, $P(A\cap B)=P(A)\times P(B)$.

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

We get $P(B)=\frac{P(A\cap B)}{P(A)}$.

Step3: Substitute the given values

Given $P(A)=\frac{1}{6}$ and $P(A\cap B)=\frac{1}{8}$, then $P(B)=\frac{\frac{1}{8}}{\frac{1}{6}}=\frac{1}{8}\times6=\frac{6}{8} = 0.75$.

Answer:

D. 0.75