52, The National Sleep Foundation reported that 36.8% of all adults snore. Of th

Question

52, The National Sleep Foundation reported that 36.8% of all adults snore. Of the people who snore, 87% are over the age of 30, 81.5% of people in their study were over the age of 30. (a) Write the above statements in probability notation. (b) Find the probability that someone is over 30 and snores. (c) Find the probability that someone is over 30 or snores. (d) Given someone is over 30, what is the prullility that he or she snores? (e) What is the probability that someone does not snore? (f) Are snoring and being over 30 mutually exclusive events? Expla with probabilities. (g) Are snoring and being over 30 independent events? Explain with probabilities

Explanation / Answer

a)

A - snores

B - over the age of 30

P(A) = 0.368

P(B) = 0.815

P(B|A)   = 0.87

b)

P(A and B) = P(B|A) P(A) = 0.87 *0.368 =0.32016

c)

P(A or B) = P(A) + P(B) - P(A and B )

= 0.368 + 0.815 - 0.32016

= 0.86284

d)

P(A|B) = P(A and B) / P(B) = 0.32016/0.815 = 0.39283

e)

P(B') = 1 - P(B) = 1 - 0.815 = 0.185

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