Question

Refer to Question 41 above. If a white ball is selected, what is the probability that it came from Bag 3

Answer 1

We will use here Bayes’ Theorem

`"P"("E"_3/"F") = ("P"("E"_3)*"P"("F"/"E"_3))/("P"("E"_1)*"P"("F"/"E"_1) + "P"("F"/"E"_2) + "P"("E"_3)*"P"("F"/"E"_3))`

= `(3/6*1)/(1/6*0+2/6*1/3 + 3/6*1)`

= `(3/6)/(2/18 + 3/6)`

= `3/6 xx 18/11`

= `9/11`

Hence, the required probabilities are `2/11` and `9/11`.