Question

When a die was rolled 60 times, the following was observed.

$\begin{array}{ccccccc}\text{Outcome}& 1& 2& 3& 4& 5& 6\\ \text{Frequency}& 9& 10& 12& 13& 7& 9\end{array}$

(i) Which number had an experimental probability that matched the theoretical probability?

(ii) How many numbers had an experimental probability that was less than that which would have been predicted by theoretical probability?

Answer 1

To match with theoretical probability, a number should appear ten out of sixty tries.
(i) Experimental probability:$P\left(E\right)=\frac{\text{Number of trials in which the event happened}}{\text{Total number of trials}}$
$P\left(2\right)=\frac{10}{60}$
Theoretical probability:$P\left(E\right)=\frac{\text{Number of favourable outcomes}}{\text{Number of all possible}outcomes}$
Theoretical probability of getting a 2: $P\left(2\right)=\frac{10}{60}$
Thus, the value 2 had an experimental probability that matched the theoretical probability.
(ii) By inspection, we can see that the frequency of 1, 5 and 6 is less than 10 for the total of 60 tries. Thus, three numbers had an experimental probability that was less than the theoretical probability.