Answer to Question #205133 in Statistics and Probability for Shema Derrick

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: \\\\\n\n\n\nSince \\space we \\space have \\space given \\space that \n\\\\\nProbability \\space that \\space it \\space is \\space Friday \\space and \\space that \\space a \\space student \\space is \\space absent \\space = \\space 0.03 \\\\\n\nP(F\u2229A)= \\space 0.03 \\\\\n\nProbability \\space it \\space is \\space Friday \\space = \\space 0.2 \\space = \\space P(F) \\\\\n\nWe \\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. \\\\\n\nSo, \\space We \\space will \\space use \\space "Conditional \\space Probability":\n \\\\\n\\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}\n\n \\\\\nHence, \\space our \\space required \\space probability \\space is \\space 0.15."