Question

two events, a and b are independent of each other. p(a) = 1/6 and p(a and b) = 1/8. what is p(b) written as a decimal? round to the nearest hundredth, if necessary.
0.02
0.04
0.29
0.75

Explanation:

Step1: Recall the formula for independent events

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

Step2: Substitute the given values

We know that \(P(A)=\frac{1}{6}\) and \(P(A\cap B)=\frac{1}{8}\). Let \(P(B) = x\). Then \(\frac{1}{8}=\frac{1}{6}\times x\).

Step3: Solve for \(P(B)\)

To solve for \(x\), we can use the equation \(x=\frac{\frac{1}{8}}{\frac{1}{6}}\). By the rule of dividing fractions (\(\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}\)), we have \(x = \frac{1}{8}\times\frac{6}{1}=\frac{6}{8}=\frac{3}{4}= 0.75\).

Answer:

D. 0.75