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Question

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

No.ofQuestionsinaday01−56−1010+Numberofdays21053

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?

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Solution

(i) Number of days in which she gave more than 5 questions = 5 + 3 = 8

Probability that she will give more than 5 questions = 820 = 0.4

(ii) Number of days in which she gave no homework = 2

Probability that she will give no homework = 220 = 0.1

(iii) Number of days in which she gave more than 10 questions = 3

Probability that she will give more than 10 questions = 320 = 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.

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