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) $\displaystyle k = 1-(\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\ frac{1}{2})$

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

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

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

(c) Need Help!!..