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A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
pls help
there are 6 sides so 1/6 = 0.167
1/6 * 450 = 75 times in theory
67/450 = 0.149
Thank you i got a 100%
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
a. The theoretical probability of rolling a 3 is 1/6. This is because there is only one face of the cube with a 3, and the cube has a total of 6 faces. So, the probability of rolling a 3 on any given roll is 1/6.
b. The experimental probability of rolling a 3 is 67/450. This is because out of the 450 total rolls, the number 3 came up 67 times. To find the experimental probability, you divide the number of times the event occurred (67) by the total number of trials (450). This gives a result of 0.149, which when simplified to a fraction is 67/450.
a. The theoretical probability of rolling a 3 is found by dividing the number of favorable outcomes (the number of times a 3 comes up) by the total number of possible outcomes (the number of times the number cube is rolled). In this case, the number of favorable outcomes is 67 (the number of times a 3 comes up) and the total number of possible outcomes is 450 (the number of times the number cube is rolled). Therefore, the theoretical probability of rolling a 3 is 67/450.
b. The experimental probability of rolling a 3 is found by dividing the number of times a 3 actually comes up (the number of favorable outcomes) by the total number of trials or experiments conducted. In this case, the number of times a 3 comes up is 67 (as given) and the total number of trials conducted is 450 (as given). Therefore, the experimental probability of rolling a 3 is also 67/450.
So, both the theoretical and experimental probabilities of rolling a 3 are 67/450. And if you ever meet a cube that keeps rolling 3s that often, I recommend you take it to Vegas!
To solve this problem, let's first understand the theoretical probability and experimental probability.
Theoretical probability is the probability of an event occurring based on reasoning or calculations. It is usually expressed as a fraction or decimal and represents the likelihood of an event happening under ideal or idealized conditions.
Experimental probability, on the other hand, is the probability of an event determined through experimentation or actual observations. It is based on the frequency of occurrence in a real-life situation.
a. To find the theoretical probability of rolling a 3, we need to know the total number of possible outcomes and the number of favorable outcomes (rolling a 3).
Since a number cube has six sides numbered 1 to 6, there are six possible outcomes when rolling it. However, we are only interested in the outcome of rolling a 3, which occurs 67 times.
The theoretical probability can be calculated as the number of favorable outcomes divided by the number of possible outcomes:
Theoretical probability of rolling a 3 = Number of favorable outcomes / Number of possible outcomes
In this case, the number of favorable outcomes is 67 (rolling a 3) and the number of possible outcomes is 450 (total number of rolls).
Therefore, the theoretical probability can be expressed as a fraction in simplest form:
Theoretical probability of rolling a 3 = 67 / 450
b. To find the experimental probability of rolling a 3, we need to determine the frequency of rolling a 3 in the 450 rolls.
Given that the number 3 came up 67 times in the 450 rolls, we can calculate the experimental probability as the number of times the event occurred (rolling a 3) divided by the total number of trials (450 rolls):
Experimental probability of rolling a 3 = Number of times rolling a 3 / Total number of rolls
In this case, the number of times rolling a 3 is 67 and the total number of rolls is 450.
Therefore, the experimental probability can be expressed as a fraction in simplest form:
Experimental probability of rolling a 3 = 67 / 450
To summarize:
a. The theoretical probability of rolling a 3 is 67/450.
b. The experimental probability of rolling a 3 is 67/450.