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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


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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