A street performer is planning to flip a coin three ×. The coin landing heads up or tails up is equally likely. What is the probability the coin lands the same side up on all three flips?

Rationale

The probability the coin lands the same side up on all three flips is 0.25.

When flipping a fair coin three times, there are a total of \(2^3 = 8\) possible outcomes. The outcomes where the coin lands the same side up are "HHH" (three heads) and "TTT" (three tails), giving us 2 favorable outcomes. Therefore, the probability of landing the same side up is \( \frac{2}{8} = 0.25\).

A (0.75) YOUR ANSWER

This option suggests that the probability of getting the same side up on all three flips is high. However, there are only two favorable outcomes (HHH and TTT) among the total of eight possible outcomes. Thus, 0.75 does not reflect the correct likelihood of this event.

B (0.25) CORRECT

This choice correctly identifies that there are 2 outcomes (HHH and TTT) out of 8 total outcomes, leading to a probability of \( \frac{2}{8} = 0.25\). This accurately represents the chance of the coin landing the same side up in all three flips.

C (0.375) YOUR ANSWER

This option implies a higher probability than what is justified by the outcomes. The calculation of \(0.375\) does not align with the total possible outcomes and does not consider the limited cases where the coin lands the same way. Hence, it incorrectly reflects the probability of the given event.

D (0.125) YOUR ANSWER

This choice suggests a lower probability than the actual scenario. While it may represent the probability of a specific sequence occurring, such as "HHH" or "TTT" individually, it does not account for both favorable outcomes together. Therefore, it underestimates the probability of getting the same side up in all flips.

Conclusion

In summary, the probability of the coin landing the same side up on all three flips is accurately calculated as 0.25, based on the favorable outcomes relative to the total possible outcomes. The incorrect options either overestimate or underestimate this probability, failing to consider the limited nature of the favorable cases in the context of multiple flips.

A street performer is planning to flip a coin three ×. The coin landing heads up or tails up is equally likely. What is the probability the coin lands the same side up on all three flips?

The probability the coin lands the same side up on all three flips is 0.25.

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