Kostyantyn M. answered • 04/01/14
Tutor
4.9
(36)
Master of Mathematics
The probability of getting any individual question right is 25%. So, the probability of getting specifically the first r questions right and missing the rest is 0.25^r * 0.75^(n-r). But there are more ways to get r questions right than just getting the first r. There are nCr ways of selecting the r questions to get right. So the total probability of getting r questions right is nCr*0.25^r * 0.75^(n-r).
n | probability
0 | 0.05631
1 | 0.18771
2 | 0.28157
3 | 0.25028
To get less than 40%, the student must get 0, 1, 2, or 3 questions right. The probability of that is calculated by looking at each number separately and adding. The result is 0.77588.
