Module 1: Probability and relative frequency

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Towards probability with coins

The probability of an event happening will move closer to the theoretical
probability value if we conduct more trials.

The more trials we use the more results we obtain. The more results we
have then:

* the less spread there is in the relative frequency values; and

* the closer the relative frequency gets to a single final value.

Lets suppose that we throw 10 coins in the air several times. How many
Heads might we get?

On the first toss we might get 7 Heads. On that basis, we might say that
the probability of getting a Head = 0.7.

If we repeated the experiment a second time then we might get (say) 4
Heads. The experimental probability (based on our results) would be said to
equal 0.55 - a total of 11 Heads from 20 coins. The third time we might get
5 Heads. The experimental probability now equals 0.53. And a fourth time we
might get 6 Heads. The experimental probability equals 0.55.

We might continue to repeat the experiment until 100 coins had been thrown
- through 10 tosses of ten coins - and record our results.

TRIAL
NUMBER OF HEADS
TOTAL NUMBER OF HEADS
TOATAL NUMBER OF TOSSES OF COINS
EXPERTIMENTAL FREQUENCY

1
7
7
10
0.7

2
4
11
20
0.55

3
5
6
30
0.53

4
6
22
40
0.55

5
8
30
50
0.6

6
4
34
60
0.57

7
3
37
70
0.53

8
5
42
80
0.53

9
6
48
90
0.53

10
4
52
100
0.52

Typically, with more trials, the experimental probability moves closer to
the theoretical probability. Notice that the results in the last column
trend towards the probability = 0.5 for getting a Head from the toss of a
coin.

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