A grocer sells bags of 10 good but misshapen carrots that have either single or double root. It is suggested that if a carrot is misshapen, then it has a single root with probability 59%. For a randomly selected bag of mixed carrots: (a) What is the expected number of double rooted carrots? Give your answer as a rational number. (b) What is the probability that exactly half of the carrots are double rooted? Give your answer to 3dp. (© What is the probability that the bag contains either all single rooted carrots or all double rooted carrots? Give your answer to 3dp.

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A grocer sells bags of 10 good but misshapen carrots that have either single or double root.
It is suggested that if a carrot is misshapen, then it has a single root with probability 59%.
For a randomly selected bag of mixed carrots:
(a) What is the expected number of double rooted carrots? Give your answer as a rational number.
(b) What is the probability that exactly half of the carrots are double rooted? Give your answer to 3dp.
(c) What is the probability that the bag contains either all single rooted carrots or all double rooted carrots? Give your answer to 3dp.
(d) From experience, the grocer believes that average weight of a single carrot is 86g with a variance of 9g. What is the expectation and variance for the net weight of the 10 carrots within the
bag. Give your answers as integers.
Expectation:
Variance:
Transcribed Image Text:A grocer sells bags of 10 good but misshapen carrots that have either single or double root. It is suggested that if a carrot is misshapen, then it has a single root with probability 59%. For a randomly selected bag of mixed carrots: (a) What is the expected number of double rooted carrots? Give your answer as a rational number. (b) What is the probability that exactly half of the carrots are double rooted? Give your answer to 3dp. (c) What is the probability that the bag contains either all single rooted carrots or all double rooted carrots? Give your answer to 3dp. (d) From experience, the grocer believes that average weight of a single carrot is 86g with a variance of 9g. What is the expectation and variance for the net weight of the 10 carrots within the bag. Give your answers as integers. Expectation: Variance:
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