Question

A,B, and C play a game and chances of their winning it in an attempt are 2/3,1/2 and 1/4 respectively. A has the first chance, followed by B and then by C. This cycle is repeated till one of them wins the game. Find their respective chances of winning the game.

Answer 1

To find their respective chances of winning the game, we need to consider the probabilities of each player winning on each attempt.

Step-by-step explanation:

To find their respective chances of winning the game, we can consider the following scenarios:

1. A wins on the first attempt with a probability of 2/3.
2. A doesn't win on the first attempt and B wins on the second attempt with a probability of (1 - 2/3) * 1/2.
3. A and B don't win on the first two attempts and C wins on the third attempt with a probability of (1 - 2/3) * (1 - 1/2) * 1/4.
4. This pattern can continue until one of them wins the game.

So, A's chances of winning the game can be calculated as the sum of these probabilities. Similarly, we can calculate the chances of B and C winning the game.

Learn more about Chances of winning the game