Unit 21 Section 5 : Estimating the Number of Successes
If we know the probability of an event, we can estimate the number of times we expect that event to take place.
For example, imagine we are flipping an unbiased coin:
The probability of "heads" is ½ and the probability of "tails" is ½.|
This means that if we flip this coin several times, we expect it to land on "heads" for half of the time.
If we flip the coin 100 times, we would expect it to land on "heads" 50 times, because ½ × 100 = 50.
If we flip the coin 500 times, we would expect it to land on "heads" 250 times, because ½ × 500 = 250.
The general rule for similar situations is:
Expected number of successes = probability of success × total number of trials
Now consider this case involving two tennis players:
The probability of Fred beating Asif at tennis is ¼.|
This means that if they play tennis several times, we expect Fred to win a quarter of the time.
If they play 20 matches, how many matches would we expect Fred to win?
Using the formula above:
Expected number of wins by Fred = probability of Fred winning × total number of games
We would expect Fred to win 5 times, because ¼ × 20 = 5.
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You roll a fair dice 120 times.
How many times would you expect to obtain:
(a) the number 6?
(b) a multiple of 3?
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You have now completed Unit 21 Section 5
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Produced by A.J.Reynolds January 2001