Buying Chocolate Ice-Cream
Trial Outcome
1 1
2 834476663355585680
3 3867670
4 82
5 830
6 31
7 1
8 38836392
9 3790
10 48560
11 1
12 0
13 991
14 5470
15 392
If 30% of the people who shop at a local grocery store buy chocolate ice-cream, what is the probability that it will take at least 5 customers to find one who buys chocolate ice-cream?
Heather set up a simulation using a random digits table select one digit numbers where 0-2 is a customer who buys chocolate ice cream and 3-9 is a customer who does not. Keep selecting one digit numbers until you get a 0-2. Record the number of digits selected.
Her results are shown in the table after 15 trials. What is the probability that it will take at least 5 customers to find one who buys chocolate ice cream?
A. 4/15
B. 8/15
C. 11/15
D. 14/15
To find the probability of taking at least 5 customers to find one who buys chocolate ice cream, we need to calculate the probability of not finding a buyer in the first 4 customers.
The probability of not finding a buyer in one trial is 70% (100% - 30%).
So, the probability of not finding a buyer in 4 trials is (0.7)^4 = 0.2401
Therefore, the probability of finding a buyer in the first 4 customers is 1 - 0.2401 = 0.7599
The probability of taking at least 5 customers to find one who buys chocolate ice cream is 0.7599, which is equal to 11/15.
Therefore, the answer is C. 11/15.