Question

According to the British United Provident Association, a major health care provider in the U.K., snoring can be an indication of sleep apnea which can cause chronic illness if left untreated. In the United States, the National Sleep foundation reports that 36.8% of the 995 adults they surveyed snored. Of the respondents, 81.5% were over the age of 30, and 32% were both over the age of 30 and snorers.

a. Are the two events of being older than 30 and “did not snore, mutually exclusive? (prove mathematically)

b. Is snoring independent of age? Explain and prove mathematically.

Answer 1

a) P(older than 30 and did not snore) = P(older than 30) - P(older than 30 and snore)

                                                            = 0.815 - 0.32

                                                            = 0.495

Since P(older than 30 and did not snore) 0, so these two events are not mutually exclusive.

b) P(Snoring) * P(older than 30) = 0.368 * 0.815 = 0.2999

P(Snoring and older than 30) = 0.32

Since P(Snoring and older than 30) P(Snoring) * P(older than 30), so the event snoring is not independent of age.