Question

The probability that it is Friday and that a student is absent is 0.03. Since there are 5 school days in a week, the probability that it is Friday is 0.2. What is the probability that a student is absent given that today is Friday?

Answer 1

$Answer: \\ Since \space we \space have \space given \space that \\ Probability \space that \space it \space is \space Friday \space and \space that \space a \space student \space is \space absent \space = \space 0.03 \\ P(F∩A)= \space 0.03 \\ Probability \space it \space is \space Friday \space = \space 0.2 \space = \space P(F) \\ We \space need \space to \space find \space the \space probability \space that \space a \space student \space is \space absent \space given \space that \space today \space is \space Friday. \\ So, \space We \space will \space use \space "Conditional \space Probability": \\ \begin{gathered}P(A|F)=\dfrac{P(F\cap \space A)}{P(F)}\\\\P(A|F)=\dfrac{0.03}{0.2}\\\\P(A|F)=0.15\end{gathered} \\ Hence, \space our \space required \space probability \space is \space 0.15.$