Question

question 6 of 10
harriet buys lunch at school every day. she always gets pizza when it is available. the cafeteria has pizza about 80% of the time.
harriet runs a simulation to model this using a random number generator. she 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.
19223 73676 45467 52711 95592
68417 82739 60940 36009 38448
what is the estimated probability that harriet will eat pizza for lunch every day next week?
a. 0.5
b. 0.4
c. 0.0
d. 0.7

Explanation:

Step1: Count total simulations

There are 10 simulation results (5 in first row, 5 in second row).

Step2: Check which simulations have all pizza (digits 2 - 9)

• 19223: has 1 (no pizza)
• 73676: all 2 - 9? 7,3,6,7,6 – yes
• 45467: 4,5,4,6,7 – yes
• 52711: has 1 (no pizza)
• 95592: 9,5,5,9,2 – yes
• 68417: has 1 (no pizza)
• 82739: 8,2,7,3,9 – yes
• 60940: has 0 (no pizza)
• 36009: has 0 (no pizza)
• 38448: 3,8,4,4,8 – yes

Wait, no – wait, each simulation is a week (5 days). Wait, the digits are for each day. So each 5 - digit number is 5 days. We need to check if in a 5 - digit number, all digits are 2 - 9 (i.e., no 0 or 1).

Let's re - check each 5 - digit number:

1. 19223: digits 1,9,2,2,3. Has 1 (no pizza) → invalid
2. 73676: 7,3,6,7,6 → all 2 - 9 → valid
3. 45467: 4,5,4,6,7 → all 2 - 9 → valid
4. 52711: 5,2,7,1,1 → has 1 → invalid
5. 95592: 9,5,5,9,2 → all 2 - 9 → valid
6. 68417: 6,8,4,1,7 → has 1 → invalid
7. 82739: 8,2,7,3,9 → all 2 - 9 → valid
8. 60940: 6,0,9,4,0 → has 0 → invalid
9. 36009: 3,6,0,0,9 → has 0 → invalid
10. 38448: 3,8,4,4,8 → all 2 - 9 → valid

Wait, no, earlier count was wrong. Let's list valid (all 2 - 9, no 0 or 1):

• 73676: valid
• 45467: valid
• 95592: valid
• 82739: valid
• 38448: valid

Wait, that's 5? Wait no, let's check again:

1. 19223: 1 (invalid)
2. 73676: 7,3,6,7,6 – no 0/1 → valid (1)
3. 45467: 4,5,4,6,7 – valid (2)
4. 52711: 1 – invalid
5. 95592: 9,5,5,9,2 – valid (3)
6. 68417: 1 – invalid
7. 82739: 8,2,7,3,9 – valid (4)
8. 60940: 0 – invalid
9. 36009: 0 – invalid
10. 38448: 3,8,4,4,8 – valid (5)

Wait, no, wait 73676: 7,3,6,7,6 – all 2 - 9? 7 is 2 - 9, 3 is 2 - 9, yes. 45467: 4,5,4,6,7 – yes. 95592: 9,5,5,9,2 – yes. 82739: 8,2,7,3,9 – yes. 38448: 3,8,4,4,8 – yes. Wait, that's 5? But wait the options are 0.5, 0.4, 0.0, 0.7. Wait, maybe I made a mistake. Wait, let's re - check each number:

1. 19223: digits 1,9,2,2,3. 1 is 0 - 1 (no pizza). So invalid.
2. 73676: 7,3,6,7,6. All 2 - 9. Valid (1)
3. 45467: 4,5,4,6,7. All 2 - 9. Valid (2)
4. 52711: 5,2,7,1,1. 1s. Invalid.
5. 95592: 9,5,5,9,2. All 2 - 9. Valid (3)
6. 68417: 6,8,4,1,7. 1. Invalid.
7. 82739: 8,2,7,3,9. All 2 - 9. Valid (4)
8. 60940: 6,0,9,4,0. 0s. Invalid.
9. 36009: 3,6,0,0,9. 0s. Invalid.
10. 38448: 3,8,4,4,8. All 2 - 9. Valid (5)

Wait, 5 valid out of 10? But 5/10 = 0.5. But wait the options have 0.5 as option A. Wait, but let's check again. Wait, maybe I miscounted. Wait the first row: 19223, 73676, 45467, 52711, 95592 (5 numbers). Second row: 68417, 82739, 60940, 36009, 38448 (5 numbers). Total 10.

Now, which of these 10 have all digits 2 - 9 (no 0 or 1):

• 73676: yes
• 45467: yes
• 95592: yes
• 82739: yes
• 38448: yes

Wait, that's 5. 5/10 = 0.5. So the estimated probability is 0.5.

Answer:

A. 0.5