A particular employee arrives at work sometime between 8:00 a.m. and 8:50 a.m. Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:50 a.m. Find the probability that the employee will arrive between 8:05 a.m. and 8:40 a.m. Round your answer to four decimal places, if necessary.

To find the probability that the employee will arrive between 8:05 a.m. and 8:40 a.m., we need to determine the length of the interval between 8:05 a.m. and 8:40 a.m. out of the total length of the interval between 8:00 a.m. and 8:50 a.m.

The length of the interval between 8:00 a.m. and 8:50 a.m. is 50 minutes (8:50 a.m. - 8:00 a.m. = 50 minutes).

The length of the interval between 8:05 a.m. and 8:40 a.m. is 35 minutes (8:40 a.m. - 8:05 a.m. = 35 minutes).

To determine the probability, we divide the length of the interval between 8:05 a.m. and 8:40 a.m. by the length of the interval between 8:00 a.m. and 8:50 a.m.:

$$\text{Probability} = \frac{\text{Length of interval between 8:05 a.m. and 8:40 a.m.}}{\text{Length of interval between 8:00 a.m. and 8:50 a.m.}}$$

$$\text{Probability} = \frac{35}{50}$$

Simplifying,

$$\text{Probability} = 0.7$$

Answer: The probability that the employee will arrive between 8:05 a.m. and 8:40 a.m. is 0.7.