Experimental Probability

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.

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 =

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

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.

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 =

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 =