Determine whether the statements below are true or false. If a statement is false, provide the correct information or revise the statement to make it correct.

A student uses the product rule to predict that the probability of flipping a coin twice and getting a head and then a tail is 1/4.

Key Concepts

Product Rule in Probability

The product rule in probability states that the probability of two independent events both occurring is the product of their individual probabilities. For example, if the probability of flipping a head on a coin is 1/2 and the probability of flipping a tail is also 1/2, the probability of both events occurring in sequence is (1/2) * (1/2) = 1/4.

Independent Events

Independent events are those whose outcomes do not affect each other. In the context of coin flips, the result of the first flip does not influence the result of the second flip. This independence is crucial for applying the product rule correctly when calculating probabilities.

Sample Space

The sample space is the set of all possible outcomes of a probability experiment. For flipping a coin twice, the sample space includes four outcomes: HH (head-head), HT (head-tail), TH (tail-head), and TT (tail-tail). Understanding the sample space helps in accurately calculating probabilities and verifying the correctness of statements regarding outcomes.