Question 213906: 1. You become suspicious when a genetics researcher selects groups of 20 newborn babies and seems to consistently get 10 girls and 10 boys. The researcher explains that it is common to get 10 boys and 10 girls in such cases.
(a) If 20 newborn babies are randomly selected, how many different gender sequences are possible?
(b) How many different ways can 10 boys and 10 girls be arranged in a sequence?
(c) What is the probability of getting 10 girls and 10 boys when 20 babies are born?
(d) Based on the preceding results, do you agree with the researcher’s explanation that it is common to get 10 boys and 10 girls when 20 babies are randomly selected?
2. Assume that you alarm clock has a 0.975 probability of working on any given morning. Determine the probability that
(a) your alarm clock will not work on the morning of an important final exam
(b) if you had two such alarm clocks, they both would fail on the morning of an important final exam
(c) you would be awakened by the alarm if you had two such clocks.
3. Singing legend Frank Sinatra recorded 381 songs. From a list of his top ten songs, 3 are to be selected as a medley tribute at the next music awards. Determine the number of different medleys possible.
4. Use a simulation of 20 families to estimate the probability of having at least 3 girls in a family of 5.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! You become suspicious when a genetics researcher selects groups of 20 newborn babies and seems to consistently get 10 girls and 10 boys. The researcher explains that it is common to get 10 boys and 10 girls in such cases.
(a) If 20 newborn babies are randomly selected, how many different gender sequences are possible?
Ans: 2^20
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(b) How many different ways can 10 boys and 10 girls be arranged in a sequence?
Ans: 20!
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(c) What is the probability of getting 10 girls and 10 boys when 20 babies are born?
Ans: 20C10(1/2)^10*(1/2)^10
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(d) Based on the preceding results, do you agree with the researcher’s explanation that it is common to get 10 boys and 10 girls when 20 babies are randomly selected?
Comment: I'll leave that to you.
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2. Assume that you alarm clock has a 0.975 probability of working on any given morning. Determine the probability that
(a) your alarm clock will not work on the morning of an important final exam
Ans: 1-0.975
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(b) if you had two such alarm clocks, what is the probability they both would fail on the morning of an important final exam.
Ans: (1-0.975)^2
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(c) you would be awakened by the alarm if you had two such clocks.
Ans: P(at least one will work) = 1 - P(both fail)
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3. Singing legend Frank Sinatra recorded 381 songs. From a list of his top ten songs, 3 are to be selected as a medley tribute at the next music awards. Determine the number of different medleys possible.
Ans: 381C3
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4. Use a simulation of 20 families to estimate the probability of having at least 3 girls in a family of 5.
Comment: I'll leave that to you.
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Cheers,
Stan H.
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