 # 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.

 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 Approximate the probability of a chance event by collecting and interpreting data - 1 of 4
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
Approximate the probability of a chance event by collecting and interpreting data - 2 of 4

Approximate the probability of a chance event by collecting and interpreting data - 3 of 4
Approximate the probability of a chance event by collecting and interpreting data - 4 of 4

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