Question 1

Tamara is not successful on her first serve but successful on her second serve 24% of the time.

To find the percentage of the time Tamara is not successful on her first serve but successful on her second serve, we need to calculate the probability of her missing the first serve and making the second. This is achieved by multiplying the probability of missing the first serve (30%) by the probability of making the second serve (80%).

A) 5%

This option does not accurately reflect the calculations needed for the scenario. The percentage of time Tamara is not successful on her first serve is not low enough to yield only 5% when considering the success rate of the second serve.

B) 14%

While 14% may seem plausible, it still does not correlate with the computation of the probabilities involved. The calculation shows that the combined probability is greater than this figure, making it incorrect.

C) 24%

This option is correct as it results from the calculation of Tamara missing her first serve (30%) multiplied by her success on the second serve (80%). Thus, 0.30 * 0.80 = 0.24, or 24%.

D) 50%

This option is incorrect since it overestimates the likelihood of Tamara's success on the second serve while underestimating the failure rate on the first serve. The computations do not support such a high percentage.

E) 56%

This option also does not reflect the realities of the scenario. The percentage calculated for the combined event does not approach 56%, making this choice incorrect.

Conclusion

The correct answer, 24%, is derived from the accurate multiplication of the probabilities involved in the scenario. All other options fail to align with the mathematical calculations necessary to determine the outcome of Tamara's serving success, confirming that C is the only valid choice.