The student solved 85 of the 100 math problems given by the teacher. 4 math problems chosen by the teacher. Find the probability that the student solved of 3.

Question

i need help with this problem

Answer 1

Probability of solving one problem=85/100=0.85. Let p=0.85. The probability of failing to solve a problem is 1-p=0.15. Let q=0.15, then (p+q)⁴=1 represents all possible outcomes.

(p+q)⁴=p⁴+4p³q+6p²q²+4pq³+q⁴=1.

In words, these terms represent:

all questions correct

3 correct, 1 wrong

2 correct, 2 wrong

1 correct, 3 wrong

all wrong

So exactly three correct is the second term 4p³q=4(0.85)³(0.15)=0.368 or 36.8% approx.