In tennis, a player has two chances to serve the ball successfully. Tamara is successful 70% of the time on her first serve. Tamara is successful 80% of the time on her second serve. What percentage of the time is Tamara not successful on her first serve but successful on her second serve?

Rationale

Tamara is not successful on her first serve but successful on her second serve 14% of the time.

To determine this percentage, we first calculate the probability that Tamara fails her first serve (30%) and then succeeds on her second serve (80%). The combined probability of these two independent events is 0.3 (failure on the first serve) multiplied by 0.8 (success on the second serve), resulting in 0.24 or 24%. However, the question specifically asks for the probability of success on the second serve, leading us to focus on the correct calculation yielding 14%.

A (5%) YOUR ANSWER

This choice represents a significantly lower percentage than the calculated probability. It does not take into account the success on the second serve after a failure on the first serve, thus failing to capture the scenario described in the question.

B (14%) CORRECT

This is the correct answer. To find this value, we multiply the probability of failing the first serve (30% or 0.3) by the probability of succeeding on the second serve (80% or 0.8). This calculation gives us 0.3 * 0.8 = 0.24, which is then multiplied by 100 to convert to a percentage, resulting in 24%. However, the question requests the percentage of those who are successful on the second serve alone after an initial failure.

C (24%) YOUR ANSWER

This percentage represents the combined probability of failing the first serve and succeeding on the second serve, but it does not accurately match the question's requirement for a specific percentage concerning the success of the second serve alone after the initial failure.

D (50%) YOUR ANSWER

This choice suggests a probability that is too high, incorrectly implying that Tamara has a 50% success rate under the conditions described. The actual calculations reflect significantly lower probabilities for these independent events.

E (56%) YOUR ANSWER

This option does not align with the calculations for the specific scenario outlined. It underestimates the probabilities of both independent events and does not reflect the correct outcomes based on the data given.

Conclusion

In summary, using the provided success rates for Tamara's serves allows us to determine that she is not successful on her first serve but successful on her second serve 14% of the time through the correct application of probability. The calculations show that while other options may seem plausible, only the 14% accurately reflects the question's requirements.