Probability

[匿名]

2010-12-11 4:05 pm

Probability that Bob and Ron can correctly forecast a horse race result is 0.5 and 0.7 respectively. Assume probability is independent from race to race. Find the probability that :
(a) Both of them make the first correct forecast on the 3rd race.
(b) Both make correct forecast simultaneously only for the first time on the 3rd race.

更新1:

To : 自由自在. Can you please explain the difference between " probability that they make incorrect forecast at the same time " and " probability that they do not make correct forecast simultaneously", thanks.

回答 (1)

用戶9112

2010-12-11 5:14 pm

✔ 最佳答案

(a) Probability that they make incorrect forecast at the same time= (1-0.5)(1-0.7) = 0.15Probability that they make correct forecast at the same time= (0.5)(0.7) = 0.35Probability that they both make the 1st correct forecast on the third race = (0.15^2)(0.35) = 0.007875(b) Probability that they do not make correct forecast simultaneously= 1 – 0.35 = 0.65Required probability = (0.65^2)(0.35) = 0.147875

2010-12-11 10:41:22 補充：
When they make incorrect forecast at the same time, that means Bob is wrong and Ron is wrong.
When they do not make correct forecast simultaneously, there are 3 situations:
1. Both of them are wrong
2. Bob is right and Ron is wrong
3. Ron is right and Bob is wrong

👍 0 👎 0