# 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.
Practice Questions
Work out the answers to the question below, then click to see whether you are correct.

You roll a fair dice 120 times.
How many times would you expect to obtain:
(a) the number 6?

(b) a multiple of 3?

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Question 1
You are planning to roll an unbiased dice 600 times.

How many times would you expect to obtain:
(a) the number one?

(b) an even number?

(c) an odd number?

(d) a number less than 3?

Question 2
A spinner is marked with the numbers 1 to 5, each of which is equally likely to occur when the spinner is spun.

If it is spun 200 times, how many times would you expect to obtain:
(a) the number five?

(b) an even number?

(c) a number less than 3?

(d) a prime number?

Question 3
 The probability that it rains on a day in September is 1 . 5
On how many days in September would you expect it to rain?

Question 4
 When you open a packet of sweets and take one out at random, the probability that it is blue is 1 . 8
If you open 40 packets of sweets, how many times would you expect to take out a blue sweet first?

Question 5
 Some crisp packets contain prizes. The probability that you find a prize in a crisp packet is 1 . 25
How many prizes would you expect to find if you opened:
(a) 50 packets?

(b) 200 packets?

(c) 1000 packets?

Question 6
 The probability that Joshua misses the school bus is 3 . In a school year there are 40 weeks, each of 5 days. 10
How many times can you expect Joshua to miss the bus in:
(a) a 12-week term?

(b) a school year?

You have now completed Unit 21 Section 5
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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