PROBABILITY AND STATISTICS

Probability problems may involve interpreting statistical data.

Example :

40 students were given a test. The table below shows the cumulative frequency of the results obtained.

a) State the probability that a student chosen at random will have a mark less than or equal to 60.

b) Two students are chosen at random from the 40 students. Find the probability that neither have marks more than 60.

c) A second group of students were tested and one-fifth of them scored more than 70 marks. If a student is now chosen at random from each group, find the probability that at least one student would have scored more than 70

Solution:

a) From the table, we see that there were 24 students who scored 60 marks or less. Therefore, the probability of selecting a student with 60 marks or less

b) Neither have marks more than 60 means that both have marks less than or equal to 60.

Probability =

c) From the table, we can work out that there are 40 – 30 = 10 students with greater than 70 marks. Therefore, the probability of selecting a student in the first with greater than 70 marks

Probability that at least one student would have scored more than 70 is

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