Question

50 students in a class were given a test containing 5 questions. The number of students who answered different number of questions are given.

$\begin{array}{cc}\text{Number of questions}& \text{Frequency}\\ 0& 3\\ 1& 6\\ 2& 8\\ 3& 15\\ 4& 16\\ 5& 2\end{array}$

(i) Find the probability of picking a student who answered all five questions;

(ii) Find the probability of picking a student who answered not less than three;

(iii) Find the probability of picking a student who answered none of the questions. [3 MARKS]

Answer 1

Concept: 1.5 Marks
Solution: 0.5 Mark each


Probability of picking a student who answered all five =$\frac{2}{50}$ = 0.04
Probability of picking a student who answered not less than three = $\frac{(2+16+15)}{50}$ = $\frac{33}{50}$ = 0.66
Probability of picking a student who answered none = $\frac{3}{50}$ = 0.06