probability (1 Viewer)

[nrumble42]

A and B take turns at throwing two dice, and a prize is won by the first player to throw a total of 8. A throws first.

i) What is the probability that A wins on his second throw?
ii) Show that the probability that A wins the prize is 36/67

 

[pikachu975]

i) To get a total of 8, 2+6, 3+5, 4+4, 5+3, 6+2, 5 ways.
Total number of ways to roll numbers is 6x6 = 36
So probability of winning on a turn is 5/36

P(Win on turn 2) = P(Lose, lose, win) = 31/36 x 31/36 x 5/36 = 4805/46656

ii) 36/67

If we take a series for A winning:
5/36 + (31/36)^2 (5/36) + (31/36)^4 (5/36)....

From this the common ratio is (31/36)^2

Now take the sum to infinity

S = a/(1-r)
= (5/36)/(1-(31/36)^2)
= 36/67 QED