quize-quants

sandipkumarshaw
Good Student
Posts: 25
Joined: Thu Jan 30, 2014 3:37 pm

quize-quants

Postby sandipkumarshaw » Fri Feb 14, 2014 4:59 pm

Three traders, Amit, Balram and Chandok play a game of dice. Whoever throws a "6" first wins the game. Amit starts the game. What is the probability of Amit winning the game?
Choose one answer.
a. 36/91 Correct
b. 25/91 Incorrect
c. ½ Incorrect
d. 1/3 Incorrect
The correct answer is A
Reason: P(A wins) = P(6) + P(not 6, not 6, not 6, 6) + P(not 6, not 6, not 6, not 6, not 6, not 6, 6) +
= 1/6 + (5/6)^3*1/6 + ... {GP with r = (5/6)^3}
= 36/91
I'm unable to understand the solution given above. Please explain it a simple way.

pradeeppdy
Finance Junkie
Posts: 258
Joined: Thu Sep 20, 2012 3:42 pm

quize-quants

Postby pradeeppdy » Thu Feb 20, 2014 12:14 pm

We can count the probability of Amit winning by making a geometric progression =
1/6+(5/6*5/6*5/6*1/6)+(5/6*5/6*5/6*5/6*5/6*5/6*1/6)........................................................(We have created G.P series)
1/6+(5/6)^3*1/6 + (5/6)^6*1/6 = 36/91


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