Which of the following is an example of a dependent event?
A. flipping two coins
B. rolling a number cube and spinning a spinner
C. choosing a card from a deck, replacing it, then choosing another card
D. choosing a cookie at random, eating it, and then choosing another at random
D. choosing a cookie at random, eating it, and then choosing another at random is an example of a dependent event because the probability of choosing the second cookie is affected by the choice of the first cookie. If the first cookie is eaten, then there is one less cookie to choose from for the second choice, affecting the probability of choosing a specific cookie.
A. flipping two coins
To determine which of the options is an example of a dependent event, let's understand what a dependent event means. In probability, dependent events are events in which the outcome of one event affects the outcome of the other event.
A. Flipping two coins: This is an example of an independent event because the outcome of one coin flip does not affect the outcome of the other coin flip.
B. Rolling a number cube and spinning a spinner: This could be an example of either dependent or independent events depending on the specific rules. If the result of rolling the number cube doesn't impact the outcome of spinning the spinner, then it would be an example of independent events. However, if the result of rolling the number cube affects or determines the possible outcomes of spinning the spinner, it would be an example of dependent events.
C. Choosing a card from a deck, replacing it, then choosing another card: This is an example of an independent event because replacing the card after the first selection restores the deck to its original state, so the outcome of the first card selection doesn't influence the probabilities for the second card selection.
D. Choosing a cookie at random, eating it, and then choosing another at random: This is an example of a dependent event because eating the first cookie changes the probability distribution for the second cookie selection.
Therefore, the correct answer is D. Choosing a cookie at random, eating it, and then choosing another at random.