# A, B and C are all running in a race. Probability that A wins is twice of B's and probability that B wins is twice Cs..

71 views

A, B and C are all running in a race. Probability that A wins is twice of B's and probability that B wins is twice Cs. Find the probability of winning of A.

posted Feb 4, 2019

4/7

Let Pa, Pb and Pc be the probability of them respectively. We have then:
Pa=2Pb
Pb=2Pc
If Pc=P, then Pa=4P and Pb=2P
P+2P+4P=1 => P=1/7
Pa=4*1/7=4/7

Similar Puzzles
+1 vote

In a chess game a man plays 16 moves , one move to every piece in the following manner:
King can move 1 step in every direction
Queen can move in every direction
Rook can move straight in any direction
Bishop can move in slant squares
Knight can move 2 forward then 1 turned step
Every pawn moves 1 or 2 step forward
What is the probability that after that move all the piece are arranged in third and fourth row if initially they are arranged in first and second row as the rule of game.

+1 vote

Three men — conveniently named A, B, and C — are fighting a duel with pistols. It's A's turn to shoot.

The rules of this duel are rather peculiar: the duelists do not all shoot simultaneously, but instead take turns. A fires at B, B fires at C, and C fires at A; the cycle repeats until there is a single survivor. If you hit your target, you'll fire at the next person on your next turn.

For example, A might shoot and hit B. With B out of the picture, it would be C's turn to shoot — suppose he misses. Now it's A's turn again, and he fires at C; if he hits, the duel is over, with A the sole survivor.

To bring in a little probability, suppose A and C each hit their targets with probability 0.5, but that B is a better shot, and hits with probability 0.75 — all shots are independent.

What's the probability that A wins the duel?