Question

Question 1
(Multiple Choice Worth 2 Points)
(Experimental Probability MC)


A spinner with 4 equal sections is spun 20 times. The frequency of spinning each color is recorded in the table below.

Outcome Frequency
Pink 6
White 3
Blue 7
Orange 4

What statement best compares the theoretical and experimental probability of landing on blue?
The theoretical probability of landing on blue is one fourth, and the experimental probability is 35%.
The theoretical probability of landing on blue is one fourth, and the experimental probability is 50%.
The theoretical probability of landing on blue is one fifth, and the experimental probability is 35%.
The theoretical probability of landing on blue is one fifth, and the experimental probability is 50%.
Question 2
(Multiple Choice Worth 2 Points)
(Experimental Probability MC)


A coin is flipped 200 times. The table shows the frequency of each event.

Outcome Frequency
Heads 98
Tails 102

Determine the experimental probability of landing on heads.
102%
98%
50%
49%
Question 3
(Multiple Choice Worth 2 Points)
(Experimental Probability LC)


A number cube is tossed 60 times.

Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8

Determine the experimental probability of landing on a number greater than 5.
8 over 60
16 over 60
18 over 60
52 over 60
Question 4
(Multiple Choice Worth 2 Points)
(Experimental Probability MC)


Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.

Outcome Frequency
Green 4
Black 6
Orange 5

Based on the given frequency, determine the experimental probability of selecting an orange marble.
0.27
0.33
0.40
0.67
Question 5
(Multiple Choice Worth 2 Points)
(Experimental Probability MC)


Sandy used a virtual coin toss app to show the results of flipping a coin 50 times, 400 times, and 2,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 400 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 50 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Question 6
(Essay Worth 4 Points)
( HC)


A coin is flipped at the start of every game to determine if Team A (heads) or Team B (tails) will get the ball first.

Part A: Find the theoretical probability of a fair coin landing on heads. (1 point)
Part B: Flip a coin 14 times and record the frequency of each outcome. Determine the experimental probability of landing on heads. Please include the frequency of each outcome in your answer. (2 points)
Part C: Compare the experimental probability to the theoretical probability. (1 point)


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Answer 1

Question 1
Answer: The theoretical probability of landing on blue is one fourth, and the experimental probability is 35%.
Reason: Theoretical = 1/4 = 25%. Experimental = 7/20 = 35%.

Question 2
Answer: 49%
Reason: Experimental probability = 98/200 = 0.49 = 49%.

Question 3
Answer: 8 over 60
Reason: Numbers greater than 5 = only the 6’s: 8/60.

Question 4
Answer: 0.33
Reason: Total marbles = 4 + 6 + 5 = 15. Orange = 5/15 = 1/3 ≈ 0.33.

Question 5
Answer: Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
Reason: Larger numbers of trials generally produce experimental probabilities closer to the theoretical 0.5.

Question 6
Part A: Theoretical probability of heads = 1/2 = 0.5 (50%).

Part B: Example 14-flip result (you can perform your own flips). Example frequencies: Heads = 8, Tails = 6.
Experimental probability of heads = 8/14 = 4/7 ≈ 0.571 (57.14%).

Part C: The experimental probability (≈57.14%) is higher than the theoretical 50% by about 7.14 percentage points. With only 14 flips some deviation from the theoretical value is expected; as the number of flips increases, the experimental probability should tend to get closer to 50%.