Question

The table below gives data about the number of homework questions that the math teacher gave in the last 20 days.

$$\begin{array}{ccccc}No.ofQuestionsinaday& 0& 1-5& 6-10& 10+\\ Numberofdays& 2& 10& 5& 3\end{array}$$

Find the probability that on any given day, she will give

(i) More than 5 questions
(ii) No homework
(iii) More than 10 questions
(iv) Comparing (i) and (iii), which is greater, and why?

Answer 1

(i) Number of days in which she gave more than 5 questions = 5 + 3 = 8
Probability that she will give more than 5 questions = $\frac{8}{20}$ = 0.4
(ii) Number of days in which she gave no homework = 2
Probability that she will give no homework = $\frac{2}{20}$ = 0.1
(iii) Number of days in which she gave more than 10 questions = 3
Probability that she will give more than 10 questions = $\frac{3}{20}$ = 0.15
Comparing (i) and (iii), (i) is greater because the set of outcomes for the event in (i) is a superset of the outcomes of (iii).
In other words, if the teacher gave more than 10 questions, it implies automatically that the teacher gave more than 5 questions. Thus, the probability of giving more than 5 questions has to be greater than or equal to the probability of giving more than 10 questions.