# Dan's Segment 2

## Problems to Calculate

1. If the knight had captured a Gnome instead of a Troll, what would his chances be of crossing safely?

In this scenario, the knight only crosses safely if H3 is true.

P(H3|G) = P(G|H3)P(H3)/Sum(P(G|Hi)P(Hi)

P(H3|G) = (5/5)(3/5)/(22/25) = 15/22

2. Suppose that we have two identical boxes, A and B. A contains 5 red balls and 3 blue balls. B contains 2 red balls and 4 blue balls. A box is selected at random and exactly one ball is drawn from the box. What is the probability that it is blue? If it is blue, what is the probability that it came from box B?

P(Blue) = P(Blue|A)P(A) + P(Blue|B)P(B) = (3/8)(1/2) + (4/6)(1/2) = 25/48

P(B|Blue) = P(Blue|B)P(B)/Bayes denominator = (4/12)/(3/16+4/12) = 16/25

## In class activity

Solutions posted on Kkumar's Segment 2 page.