A deck of 10 cards labeled 1–10 is shuffled. One card is selected at random. If the experiment is repeated 120 times, how many times will you expect to select number 5?
Since there are 10 cards and each card has an equal chance of being selected, the probability of selecting number 5 is 1/10.
Expected value = probability of event x number of trials
Expected number of times 5 will be selected = (1/10) x 120 = 12.
Therefore, you can expect to select number 5 12 times out of 120 trials.
To find the number of times you would expect to select number 5 when the experiment is repeated 120 times, you need to determine the probability of selecting number 5 in a single trial.
There are a total of 10 cards in the deck and each card has an equal chance of being selected. So, the probability of selecting number 5 is 1/10.
To find the expected number of times, you multiply the probability of selecting number 5 by the number of trials. In this case, it would be:
Expected number of times = Probability of selecting number 5 x Number of trials
Expected number of times = (1/10) x 120
Expected number of times = 12
Therefore, you would expect to select number 5 approximately 12 times when the experiment is repeated 120 times.
To calculate the expected number of times you will select number 5 in this experiment, we need to determine the probability of selecting number 5 in a single trial.
Since there are a total of 10 cards and they are shuffled, each card has an equal chance of being selected. Therefore, the probability of selecting any particular number (including 5) is 1/10, or 0.1.
The expected value, also known as the expected number of occurrences, can be calculated using the formula:
Expected value = Probability of occurrence * Number of trials
In this case, the probability of selecting number 5 is 0.1, and the number of trials is 120. Therefore, the expected number of times you will select number 5 can be found by:
Expected value = 0.1 * 120 = 12
Hence, you would expect to select number 5 approximately 12 times in 120 trials.