1. ## Probability Distrubtion Help!!

Question:
The probability of the scores on a biased dice are shown in the table below.

(a) Find the value of k.
Two players, Hazel and Ross, play a game with this biased dice and a fair dice. Hazel choose one of the two dice at random and rolls it. If the score is 5 or 6 wins a point.
(b) Calculate the probability that Hazel wins a point.
(c) Hazel chooses a dice, rolls it and wins a point. Find the probability that she choose the biased dice.

Attempt:
(a) $k = 1-(\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\ frac{1}{2})$

k = $\frac{1}{18}$

(b) P(Hazel wins a point) = $\frac{1}{2}\times\frac{2}{6}+\frac{1}{2}\times(\fr ac{1}{9}\times\frac{1}{2})$

P(Hazel wins a point) = $\frac{17}{36}$

(c) Need Help!!..

2. You have done both parts correctly.
In part b) you found P(W).

For part c) you need $P(B|W) = \frac{{P(B \cap W)}}{{P(W)}} = \frac{{P(W|B)P(B)}}{{P(W)}}$.