Answer: the value of P(B) = [tex]\dfrac{1}{3}[/tex] .
Step-by-step explanation:
If A and B are two independent events, then P(A and B)=P(A) x P(B) (i)
Given the following probabilities : [tex]P(A)=\dfrac{1}{2},\ \ P(\text{A and B})=\dfrac{1}{6}[/tex]
To find : [tex]P(B)[/tex] such that events A and B are independent
Put all values in (i), we get
[tex]\dfrac{1}{6}=\dfrac{1}{2}\times P(B)\\\\\Rightarrow\ P(B)=\dfrac{2}{6}\\\\\Rightarrow\ P(B)=\dfrac{1}{3}[/tex]
Hence, the value of P(B) = [tex]\dfrac{1}{3}[/tex] .
