In which scenario is the experimental probability equal to the theoretical probability?
The experimental probability is equal to the theoretical probability if the actual results of the experiment are consistent with the expected results predicted by the theoretical probability. This means that the experiment would need to be repeated many times and the frequency of the desired outcome would approach the predicted probability.
A survey was conducted to determine peoples favorite activities during winter. Suppose only three answer options were given building a snowman, skiing, and sledding. If 900 people responded, how many would been expected to choose building a snowman as their favorite activity?
We are not given any information about how many people chose each activity, but we can determine the expected number of people who chose building a snowman if we assume that each activity was equally likely to be chosen.
Since there were three choices, each one would have a probability of 1/3 of being chosen. To find the expected number of people who chose building a snowman, we multiply the total number of respondents by the probability of choosing building a snowman:
Expected number of people who chose building a snowman = (total number of respondents) x (probability of choosing building a snowman)
Expected number of people who chose building a snowman = 900 * (1/3)
Expected number of people who chose building a snowman = 300
Therefore, if each activity was equally likely to be chosen, we would expect approximately 300 people to choose building a snowman.
The letter tiles C, A, R, E, S are placed in a box. Without looking, Jarrell picks a letter tile from the box and records the results before placing it back. If your repeats the procedure 100 times, how many times with the letter A tile be picked?
Since there are five letter tiles in the box and Jarrell is replacing the tile after each pick, the probability of picking the letter A on any given pick is 1/5.
If Jarrell repeats the procedure 100 times, we can use the formula for expected value or the mean to determine the expected number of times the letter A will be picked:
Expected number of times the letter A is picked = (total number of picks) x (probability of picking A on any given pick)
Expected number of times the letter A is picked = 100 x (1/5)
Expected number of times the letter A is picked = 20
Therefore, we would expect the letter A to be picked approximately 20 times in 100 picks if the probability of picking any letter is equal. However, since this is a probability experiment, it is possible that the actual number of times the letter A is picked could be more or less than 20.
The letter tiles W, I, S, D, O, M are placed on a box. Without looking, Abby picks a letter from the box. What is the probability that the letter she picks is a vowel? Write your answer in the simplest form of a fraction.
There are six tiles in the box and we need to determine the probability that Abby picks a vowel. Vowels are the letters I and O.
The probability of picking a vowel on any given pick is the number of vowels in the box divided by the total number of tiles in the box:
Probability of picking a vowel = (number of vowels) / (total number of tiles)
Probability of picking a vowel = 2 / 6
Probability of picking a vowel = 1/3
Therefore, the probability that Abby picks a vowel is 1/3.