Jacob performed an experiment with a weighted die, numbered 1 to 6. He rolled the die 125 times and recorded the results. Complete the table below.
0.104
0.232
24
0.048
0.176
22
18
37
B. No, because although it is probable the arrow will land in the purple section, it is not fact.
While it is probable that the arrow will land in the purple section since it is larger, it is not a fact until the arrow is spun and lands on a specific section. Probability deals with likelihood or chance, not certainty.
Megan tells her friends that if she spins the arrow shown, it is a fact that the arrow will not land on the green section. Is she right?
A. Yes, because it is a fact that the arrow will land on the largest area, which is the purple section.
B. No, because although it is probable the arrow will land in the purple section, it is not fact.
C. Yes, because probability is fact, the arrow will land on the purple section.
D. No, because the arrow will land on a green section 50% of the time and a purple section 50% of the time.
The names of five students are put into a bag. Mrs. Parsons will randomly draw one name from the bag each day to decide who will help pass out papers. The student's name is then returned back into the bag.
The table shows the number of times each student's name was drawn.
Select the name of each student who was drawn at a higher rate than the theoretical probability of being drawn.
Alfred-6
Talita-9
Kurt-10
Faith-8
Neil-7
To determine the theoretical probability of each student being drawn, we divide the number of times each student's name was drawn by the total number of draws:
Total draws = 6 + 9 + 10 + 8 + 7 = 40
Theoretical probability for each student:
Alfred: 6/40 = 0.15
Talita: 9/40 = 0.225
Kurt: 10/40 = 0.25
Faith: 8/40 = 0.2
Neil: 7/40 = 0.175
The theoretical probability of each student being drawn is as follows:
Alfred: 0.15
Talita: 0.225
Kurt: 0.25
Faith: 0.2
Neil: 0.175
Comparing the theoretical probabilities with the actual number of times each student's name was drawn:
Alfred: Drawn 6 times (Theoretical probability: 0.15)
Talita: Drawn 9 times (Theoretical probability: 0.225)
Kurt: Drawn 10 times (Theoretical probability: 0.25)
Faith: Drawn 8 times (Theoretical probability: 0.2)
Neil: Drawn 7 times (Theoretical probability: 0.175)
Based on the comparison, the students who were drawn at a higher rate than the theoretical probability of being drawn are:
- Talita (9 times drawn, theoretical probability: 0.225)
- Kurt (10 times drawn, theoretical probability: 0.25)
To complete the table, we need to determine the number of times each number (1 to 6) appeared in Jacob's experiment.
Let's first calculate the total number of times the die was rolled:
1 + 2 + 4 + 3 + 5 + 1 = 16 times
Now we can calculate the number of times each number appeared:
Number 1: 1 + 4 + 1 = 6 times
Number 2: 2 times
Number 3: 3 times
Number 4: 4 times
Number 5: 5 times
Number 6: 1 time
Now, let's complete the table:
1. 0.104 (6)
2. 0.232 (2)
3. 24 (3)
4. 0.048 (4)
5. 0.176 (5)
6. 22 (1)
7. 18
8. 37