What is the probability that he or she slept for at least 8 hours last night? (Please round your final answer to 2 decimal places)

Question

Employees from a company accepted an interview talking about their sleep last night. It is found that 80% of the employees slept for at least 8 hours last night. Among those sleeping for at least 8 hours, 70% went to bed at 11 pm, while among those sleeping for less than 8 hours, only 30% went to bed at 11 pm. Suppose a randomly chosen employee is found to go to bed at 11 pm. What is the probability that he or she slept for at least 8 hours last night? (Please round your final answer to 2 decimal places)

Answer 1

Draw a tree diagram.

> 0.7 bed at 11

0.8 > 8 hours > 0.3 not bed at 11

0.2 < 8 hours > 0.3 bed at 11

> 0.7 not bed at 11

bed at 11 and sleep > 0.8 = 0.7 * 0.8 = 0.56