Question

5. According to the American Academy of Otolaryngology, 45% of adults snore occasionally. Three adults are...

5. According to the American Academy of Otolaryngology, 45% of adults snore occasionally. Three adults are chosen at random.

a) Let Si= ith adult snores occasionally. List all the possible outcomes.

b) Find the probability that none of the adults snore occasionally.

c) Find the probability that exactly one adult snores occasionally, by calculating the sum of the probabilities of the “successful” outcomes.

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Answer #1

a)

The possible outcomes is :

S1 S253, S1S2S3, SS S3, STS2S3, SfS2S, STSS3, S1 SS, SSCSS)

Here S^{c}_{i} shows that  ith adult does not snore occasionally.

b)

Out of 8 possible outcomes, one outcome shows that none of the adults snore occasionally is

P(none of the adults snore occasionally) = 1/8 = 0.125

c)

Out of 8 possible outcomes, three outcomes shows that exactly one adult snores occasionally is

P(exactly one adult snores occasionally) = 3/8 = 0.375

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