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.
Mark |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
80 |
90 |
100 |
Number of students scoring the mark or less |
2 |
5 |
8 |
11 |
18 |
24 |
30 |
32 |
37 |
40 |
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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