If you roll a die twice, what is the probability of getting a 3 both times?

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Question: If you roll a die twice, what is the probability of getting a 3 both times?

Options:

Correct Answer: 1/36

Solution:

The probability of rolling a 3 on one die is 1/6, so for two rolls, it is (1/6) * (1/6) = 1/36.

If you roll a die twice, what is the probability of getting a 3 both times?

If you roll a die twice, what is the probability of getting a 3 both times?

Step 1: Understand that a die has 6 sides, numbered from 1 to 6.
Step 2: Determine the probability of rolling a 3 on one die. Since there is only one side with a 3, the probability is 1 out of 6, or 1/6.
Step 3: Since you are rolling the die twice, you need to find the probability of rolling a 3 on both rolls.
Step 4: To find the combined probability of two independent events (rolling a 3 on the first roll and rolling a 3 on the second roll), you multiply the probabilities of each event.
Step 5: Multiply the probability of rolling a 3 on the first roll (1/6) by the probability of rolling a 3 on the second roll (1/6). This gives you (1/6) * (1/6).
Step 6: Calculate (1/6) * (1/6) which equals 1/36.
Step 7: Conclude that the probability of rolling a 3 both times is 1/36.

Probability of Independent Events – The question tests the understanding of calculating the probability of independent events occurring in sequence.
Basic Probability Calculation – It assesses the ability to apply basic probability rules, specifically the multiplication rule for independent events.