Question

question 3 of 10
pedro buys lunch at school every day. he always gets pizza when it is available. the cafeteria has pizza about 80% of the time.
pedro runs a simulation to model this using a random number generator. he assigns these digits to the possible outcomes for each day of the week:

• let 0 and 1 = no pizza available
• let 2, 3, 4, 5, 6, 7, 8, and 9 = pizza available

the table shows the results of the simulation.

what is the estimated probability that pedro will eat pizza for lunch every day next week?
a. 0.4
b. 0.7
c. 0.3
d. 0.0

Explanation:

Step1: Determine the number of trials

There are 10 trials (the 10 five - digit numbers in the table).

Step2: Determine the number of successful trials

A successful trial is a five - digit number where all digits are in the set \(\{2,3,4,5,6,7,8,9\}\). Looking at the 10 numbers:

• \(95032\): has a \(0\) (not successful)
• \(47150\): has a \(1\) and \(0\) (not successful)
• \(71709\): has a \(0\) (not successful)
• \(38889\): all digits \(3,8,8,8,9\) (successful)
• \(94007\): has \(0\)s (not successful)
• \(35013\): has \(0\) and \(1\) (not successful)
• \(57890\): has \(0\) (not successful)
• \(72924\): all digits \(7,2,9,2,4\) (successful)
• \(19365\): has \(1\) (not successful)
• \(47879\): all digits \(4,7,8,7,9\) (successful)

The number of successful trials \(n = 3\)

Step3: Calculate the probability

The probability \(P=\frac{n}{N}\), where \(n\) is the number of successful trials and \(N\) is the total number of trials. Here \(N = 10\) and \(n=3\), so \(P=\frac{3}{10}=0.3\)

Answer:

C. \(0.3\)