Probability

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Probability
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Problem 1 a-c

• 1. Assume that you have three six-sided dice. One
  is yellow (Y), one is red (R) and one is white
  (W).
• What is the probability that, in rolling only the
  red dice, it will show the number 5?
• What is the probability that, in rolling only the
  white dice, it will show an even number?
• What is the probability that, in rolling all
  three dice at once, the outcome will be 2(Y),
  4(R), 6 (W)?

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Problem 1 d-f

• 1.   Assume that you have three six-sided dice.
  One is yellow (Y), one is red (R) and one is
  white (W).
• d.   What is the probability that, in rolling all
  three dice at once, the outcome will be 1, 3 and
  5 in any color combination?
• e.   What is the probability that, in rolling all
  three dice at once, the outcome will be the same
  number on all three dice?
• f.    What is the probability that, in rolling
  all three dice at once, the outcome will be a
  different number on all three dice?

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Problem 2

• 1.   Skittles come in yellow, orange, purple and
  green. Assume that you have three jars of
  Skittles with the following color compositions
• Jar 1 100 yellow and 400 green
• Jar 2 200 orange and 300 green
• Jar 3 50 purple and
  450 green
• If you select one Skittle from each jar
  without looking, determine the probability of
  obtaining
• a.      one yellow, one orange and one purple
  Skittle.
• b.      one orange and two green Skittles.
• c.      at least one green Skittle.
• d.      two green Skittles and one alternate
  color Skittle.
• e. one orange, one purple and one green
  Skittle.

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Problem 3

• A bent little finger is inherited with the
  autosomal dominant allele B. The autosomal
  recessive allele b codes for a straight little
  finger. Nan and her husband Nathan both have bent
  little fingers. Their first child, a son named
  Nicholas, has straight little fingers.
• What is the probability that Nan and Nathans
  second child will have bent little fingers?
• What is the probability that out of four children
  born to Nan and Nathan, 3 will have straight
  little fingers?
• What is the probability that Nan and Nathans
  second child will have straight little fingers,
  their third child will have bent little fingers
  and their fourth child will have bent little
  fingers?
• d. Out of three children born to Nan and
  Nathan, what is the probability that at least one
  will have bent little fingers?

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Problem 4

• Cystic fibrosis is inherited with the autosomal
  recessive allele c. Individuals with the
  autosomal dominant allele C do not have the
  disease. Jessica does not have cystic fibrosis
  but she has a brother with the disease. Her
  husband Jerry also does not have cystic fibrosis
  but has a sister with the disease.
• What is the probability that Jessica carries the
  c allele?
• What is the probability that Jerry carries the c
  allele?
• What is the probability that Jessica and Jerry
  could have a child with cystic fibrosis?
• Out of 3 children born to Jessica and Jerry, what
  is the probability that 2 will have cystic
  fibrosis?
• e. For Jessica and Jerry, what is the
  probability that their first child would not have
  cystic fibrosis, their second child would have
  cystic fibrosis and their third child would not
  have the disease?

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Problem 5

• Duchenne muscular dystrophy (DMD) is inherited
  with the X-linked recessive allele d. Individuals
  with the X-linked dominant allele D do not have
  the disease. Polly does not have DMD but she has
  a brother with the disease. Neither Pollys
  father nor mother has DMD. Polly marries Peter,
  who also does not have DMD.
• What is the probability that Polly carries the d
  allele?
• What is the probability that Polly and Peter can
  have a child with DMD?
• For Polly and Peter, what is the probability that
  their first child would be a daughter without
  DMD, their second child would be a son without
  the disease and their third child would be a son
  with DMD?
• Out of 5 children born to Polly and Peter, what
  is the probability that 2 will have DMD?