Answer to Question #346999 in Statistics and Probability for Nzuzi

Question

Question 1.11[4]

There are two bags of chocolates. Bag one has 5 Barones and 2 KitKats and Bag 2 has 2 Barones

and the 7 KitKats. A chocolate is selected at random from Bag one and added to Bag two. A

chocolate is now drawn randomly from Bag two. Given that the chocolate selected is a KitKat what

is the probability that the original chocolate drawn from Bag one was a Barone? Show all working

out.

Answer 1

Let $B$ denote the event "a Barone is selected at random from Bag one".

Let $K$ denote the event "a KitKat is selected at random from Bag one".

Let $k$ denote the event "a KitKat is selected at random from Bag two".

$$P(B|k)=\dfrac{P(k|B)P(B)}{P(k|B)P(B)+P(k|K)P(K)}$$

Given $P(B)=\dfrac{5}{7}, P(K)=\dfrac{2}{7},$

$P(k|B)=\dfrac{7}{2+7+1}=\dfrac{7}{10},$

$P(k|K)=\dfrac{7+1}{2+7+1}=\dfrac{8}{10}$

$$P(B|k)=\dfrac{\dfrac{7}{10}(\dfrac{5}{7})}{\dfrac{7}{10}(\dfrac{5}{7})+\dfrac{8}{10}(\dfrac{2}{7})}=\dfrac{35}{51}$$