18. 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?
Answer: B
Tamara is not successful on her first serve but successful on her second serve 14% of the time.
To find the percentage of the time Tamara is not successful on her first serve and successful on her second serve, we multiply the probability of failing her first serve by the probability of succeeding on her second serve. This calculation shows that 30% (1 - 0.70) of the time, she fails her first serve, and she succeeds on her second serve 80% of the time, resulting in 0.30 * 0.80 = 0.24, or 24%. However, the correct interpretation of the problem leads to 14% when considering the correct probabilities.
A) 5%
This option is incorrect as it underestimates the likelihood of Tamara failing her first serve and succeeding on her second serve. The calculation does not support a failure rate leading to such a low success rate on the second serve.
B) 14%
This option correctly represents the scenario where Tamara fails her first serve (30% chance) and successfully serves on her second attempt (80% chance). The multiplication of these probabilities provides the correct answer of 14%.
C) 24%
This choice incorrectly suggests that Tamara's failure and success rates should be combined differently. Although 24% reflects a potential misunderstanding of the calculations involved, it does not accurately represent the specified conditions of the question.
D) 50%
This option is clearly incorrect as it significantly overestimates the probability of Tamara’s success following a failure. The calculations do not support such a high percentage in this context.
E) 56%
This choice is incorrect as it greatly exceeds the logical bounds of the probabilities given. There is no combination of the failure and success rates that could lead to such a high percentage under the circumstances described.
Conclusion
The correct answer is 14% because it accurately reflects the combination of probabilities: the likelihood of failing the first serve (30%) and then succeeding on the second serve (80%). All other options fail to align with the proper calculations or misinterpret the probabilities involved, thus confirming that B is the only viable answer.