Three horses, A, B and C are in a race. A and B have the same probability of winning, and each is twice as likely to win as C. Find the probability of B or C winning.
A = 2C
B = 2C
A + B + C = 1
2C + 2C + C = 1
You should be able to take it from here. I hope this helps. Thanks for asking.
To find the probability of B or C winning, we need to determine their individual probabilities and then sum them up.
Let's assume the probability of C winning is x. According to the given information, both A and B have the same probability of winning, which means each of them has a probability of 2x.
The sum of the probabilities of all possible outcomes must equal 1. Since there are three horses, the total probability is:
C + (2x) + (2x) = 1
Simplifying this equation, we get:
C + 4x = 1
Now we only need to solve for x to find C's probability of winning:
5x = 1
x = 1/5
Therefore, the probability of C winning the race is 1/5.
To find the probability of B winning, we multiply x by 2:
2x = 2 * (1/5) = 2/5
Hence, the probability of B winning the race is 2/5.
Finally, to find the probability of B or C winning, we add their individual probabilities:
P(B or C) = P(B) + P(C) = 2/5 + 1/5 = 3/5
Therefore, the probability of either B or C winning the race is 3/5.