Question

From the experimental data, it is observed that there is an $80\%$ chance that ice cream will be brought by a group of children on any given day of summer. Run the simulation which has digits from 1 through 5 to find the estimate of the experimental probability that the ice cream will be brought by the children in at least 8 days of a 10-day sample.
Note: Take 1 representing ice cream not purchased.
Simulated data shows the following:

$\text{Trial}1:2,1,3,4,5,5,3,1,1,2$
$\text{Trial}2:1,2,5,4,3,5,4,2,1,3$
$\text{Trial}3:2,1,3,5,4,2,1,3,4,5$
$\text{Trial}4:1,2,5,4,3,2,5,4,3,2$
$\text{Trial}5:2,1,5,3,4,5,2,4,2,5$

• A. $60\%$
• B. $20\%$
• C. $80\%$
• D. $40\%$

Answer 1

The correct option is C $80\%$

There is an $80\%$ chance of children buying ice cream in summer which is the same as 4 out of 5 chances. Digit 1 is chosen as ice cream not being purchased by the children and all the other digits in the simulation, i.e., 2, 3, 4, and 5 as ice cream being purchased.

Running the simulation 5 times, we see in trial 2 through trial 5 that ice cream is sold at least 4 out of 5 times.

Therefore, the estimate of the probability of ice cream being purchased at 8 days out of 10 days is
$\frac{4}{5}=\frac{4}{5}\times 100=80\%$