14. 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?
Answer: B
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, or 8, possible outcomes. The outcomes where all flips are the same (either heads or tails) are two: HHH and TTT. Therefore, the probability of getting the same side on all three flips is 2 out of 8, which simplifies to 0.25.
A) 0.75
This option suggests that there is a 75% chance that the coin lands on the same side for all flips. This is incorrect, as it does not account for the specific combinations needed to achieve the same side outcome. The actual probability is much lower, as only two out of the eight possible outcomes result in the same side.
B) 0.25
This option is correct because there are only two favorable outcomes (HHH and TTT) out of a total of eight possible outcomes when flipping a coin three times. Thus, the correct probability is indeed 0.25.
C) 0.375
This option is incorrect as it implies that more than two favorable outcomes exist among the eight total outcomes. The calculation of 0.375 does not reflect the actual number of ways to have all three flips the same, which is limited to just two outcomes.
D) 0.125
This option represents a probability of 1 out of 8, suggesting only one favorable outcome exists for all flips being the same. As previously noted, there are two outcomes (HHH and TTT), making this option incorrect.
Conclusion
The correct answer is definitively B (0.25) because it accurately reflects the ratio of favorable outcomes to total outcomes in the scenario described. All other options either overestimate or underestimate the likelihood of achieving the same result in all three flips of the coin.