The theoretical probability that Spinner A lands on a "2" is 1/6, as there is only one favorable outcome (landing on a "2") out of six total outcomes (the numbers 1 to 6 on the spinner).
Similarly, the theoretical probability that Spinner B lands on a "2" is also 1/6.
The empirical probability that Spinner A lands on a "2" is calculated by dividing the number of times Spinner A landed on a "2" (14) by the total number of times it was spun (50). So the empirical probability is 14/50, which simplifies to 7/25.
The empirical probability that Spinner B lands on a "2" is calculated in the same way, dividing the number of times Spinner B landed on a "2" (19) by the total number of times it was spun (50). Therefore, the empirical probability is 19/50, which does not simplify further.
The Law of Large Numbers states that as the number of trials or experiments increases, the empirical probability of an event will approach its theoretical probability. In this spinner example, the Law of Large Numbers can be applied by spinning each spinner a large number of times, such as 500 or 1000 spins. As the number of spins increases, the empirical probabilities of landing on a "2" for both Spinner A and Spinner B should come closer to their respective theoretical probabilities of 1/6.
Spinner A and Spinner B are shown below.
The theoretical probability of an event E is
P(E)=(number of favorable outcomes)/(total number of outcomes)
What is the theoretical probability that Spinner A lands on a “2” ?
What is the theoretical probability that Spinner B lands on a “2” ?
The empirical probability of an event E is
P(E)=(number of times event E occured)/(number of times the experiment was performed)
Suppose that Spinner A is spun 50 times, and it lands on a “2” a total of 14 times. Based on these results, what is the empirical probability that Spinner A lands on a “2” ?
Suppose that Spinner B is spun 50 times, and it lands on a “2” a total of 19 times. Based on these results, what is the empirical probability that Spinner B lands on a “2” ?
Describe in your own words how the Law of Large Numbers can be applied to this spinner example.
11 answers
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11 answers