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.

Verified step by step guidance

1. Understand the problem: The student is using the product rule to calculate the probability of flipping a coin twice and getting a head followed by a tail. The product rule states that the probability of two independent events occurring together is the product of their individual probabilities.
2. Define the probabilities: For a fair coin, the probability of flipping a head (H) is 1/2, and the probability of flipping a tail (T) is also 1/2. These events are independent, meaning the outcome of the first flip does not affect the outcome of the second flip.
3. Apply the product rule: Multiply the probability of flipping a head (1/2) by the probability of flipping a tail (1/2). This gives the probability of flipping a head followed by a tail.
4. Verify the student's calculation: The student predicted the probability to be 1/4. Check if this matches the result obtained using the product rule.
5. Evaluate the statement: Determine whether the statement is true or false based on the calculation. If false, revise the statement to clarify the correct probability and reasoning.

Key Concepts

Product Rule in Probability

The product rule in probability states that the probability of two independent events occurring together 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 (head followed by tail) 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, as it allows us to multiply the probabilities of each event.

Probability of Coin Flips

When flipping a fair coin, the probability of landing on heads or tails is equal, each being 1/2. Therefore, when calculating the probability of a specific sequence of flips, such as getting a head followed by a tail, one must consider the individual probabilities of each flip and apply the product rule to find the overall probability.