1. Experimental Probability

2. Isn’t that
P(a ‘Head’) = P(a ‘Tail’) = ?
I tossed a coin twice, but I can’t get 1 head and 1 tail.
P(a ‘Head’) = P(a ‘Tail’) = is deduced from theories and is called a theoretical probability. However, in reality, when a coin is tossed twice, the result may not be 1 head and 1 tail.

3. Let’s consider the following activity.
The table below shows the result of tossing a coin 50 times.
Head
Tail
Frequency 23 27
frequency of getting a head
Then, from the table, 23
relative frequency of getting a head = 50
total frequency
and relative frequency of getting a tail =

4. In general, the relative frequency of occurrence of an event we get from an activity or experiment is called the experimental probability.
In reality, when we toss a coin several times, we do not know if we can get a ‘Head’ half of the times.
Experimental probability P(E) of an event E
number of times event E occurs in an experiment =
total number of trials

5. From the activity of tossing a coin 50 times, we can see that the experimental probability may be different from the theoretical probability. ≠
Experimental probability of getting a head = ≠
Experimental probability of getting a tail =
However, for a large number of trials, the experimental probability is close to the theoretical probability.
The experimental probability of an event may vary from experiment to experiment.

6. Follow-up question
Two coins are tossed 80 times. The results are recorded in the following table:
Result
No tails
1 tail only
2 tails
No. of occurrence 18 x 14
(a) Find the value of x. (b)
Hence, find the experimental probability of getting 1 tail only.
Solution
(a) 14 18 80 - = x 48 =

7. Follow-up question (cont’d)
Two coins are tossed 80 times. The results are recorded in the following table:
Result
No tails
1 tail only
2 tails
No. of occurrence 18 x 14
(a) Find the value of x. (b)
Hence, find the experimental probability of getting 1 tail only.
Solution 80 48 =
 x = 48
(b)
Experimental probability of getting 1 tail only 5 3 =