4條PROBABILITY問題

1)
Number of people studying only Biology and Chemistry = 12 - 5 = 7
Number of people studying only Physics and Chemistry = 14 - 5 = 9
Number of people studying only Biology and Physics = 12 - 5 = 7

Therefore, the number of people studying only one of these three subjects
= 63 - 7 - 9 - 7 - 5 = 35

The answer is hence D.

2)
If one of them wins the championship, the other two must lose.
Thus, we only need to consider the probability of winning for that person.
The required probability is given by
1/4 + 1/5 + 1/6
= 37/60

The answer is hence D.

3)
The probability for John to win
= 1/6 + (5/6)(5/6)(1/6) + (5/6)(5/6)(5/6)(5/6)(1/6) + ...
By sum of geometric sequence to infinity, we have
(1/6)/(1 - (5/6)^2)
= 6/11
Thus, the required probability
= 1 - 6/11
= 5/11

The answer is hence D.

4)
For each can, the probability for no prize can-cap = 1 - 1/10 = 0.9.
The probability for all n cans with no prize can-cap = (0.9)^n
The probability for all n cans with at least 1 prize can-cap = 1 - (0.9)^n

Now, we have
1 - (0.9)^n > 0.8
(0.9)^n < 0.2
n log 0.9 < log 0.2
n > log 0.2 / log 0.9　 　|| log 0.9 < 0
n > 15.3
Hence, the least value of n is 16.

Therefore the answer is C.