Hi, I'll take a stab at helping.
As mentioned above, the probability that Ben wins the championship is 1/7. Therefore, the probability that Ben loses the championship is 6/7 (in other words, 1- 1/7 = 6/7).
Mike has a 1/4 chance of winning. This is conditional upon Ben losing (because Ben and Mike can't both win). To calculate Mike's chances of winning, you multiply the probability that Mike wins (1/4) * the probability that Ben loses (6/7).
1/4 * 6/7 = 3/14
Repeat the same process for Rob. Multiply the probability of Ben losing times the probability of Rob winning
1/3 * 6/7 = 2/7
Simply add the two probabilities together. You add the probabilities together because the question asks what the probability that Mike
OR Rob win.
The result is 3/14 + 2/7 = 7/14 = 1/2.
As Bunuel would say, Hope this helps.
Bunuel wrote:
If Ben were to lose the championship, Mike would be the winner with a probability of \(\frac{1}{4}\), and Rob - \(\frac{1}{3}\) . If the probability of Ben being the winner is \(\frac{1}{7}\), what is the probability that either Mike or Rob will win the championship? Assume that there can be only one winner.
A. \(\frac{1}{12}\)
B. \(\frac{1}{7}\)
C. \(\frac{1}{2}\)
D. \(\frac{7}{12}\)
E. \(\frac{6}{7}\)