Question

Jada and Elena learned that 8% of students have asthma. They want to know the probability that in a team of 4 students, at least one of them has asthma. To simulate this, they put 25 slips of paper in a bag. Two of the slips say "asthma." Next, they take four papers out of the bag and record whether at least one of them says "asthma." They repeat this process 15 times. Jada says they could improve the accuracy of their simulation by using 100 slips of paper and marking 8 of them. Elena says they could improve the accuracy of their simulation by conducting 30 trials instead of 15. Do you agree with either of them?

Answer 1

By conducting 30 trials instead of 15, they would improve the accuracy of their simulation, therefore, Elena is correct

Explanation:

The parameters given are;

Jada and Elena are trying to estimate the probability that 1 in 4 students selected has asthma where the asthma prevalence rate = 8%

The experiment uses 25 slips to represent 25 students and they labelled 2 of the strips as asthma to indicate the expected number of asthma in 25 students which is 2/25 = 0.08. That is the number of asthma in 25 students is 8% of 25 = 0.08 × 25 = 2

From the 25 slips, they randomly select groups of 4 which represent the team of four students to see if any of the 4 slips is one of the two slips labelled as asthma slips

Therefore, to improve the accuracy of the estimate of the probability they should increase the number of trials from 15 to 30, hence Elena is correct.