4. Jack's sister ordered 30 bottles of wine for her birthday party. A covid lock-down caused her to cancel her (traditionally extravagant) party this year and so she could not use the wine. Instead she decided to store the wine in a spare room for 12 months and to use it next year. Unfortunately, this wine is Jack's favourite. To ensure that the wine is not spoiling in storage, Jack decides to quietly sample 5 bottles of his sisters wine. (a) How many possible ways can 5 bottles be chosen from a total of 30 if we do not care about the order in which they are chosen? (b) Over the coming year, Jack attempts to quietly sample 1 bottle per month. What is the probability that Jack samples exactly 5 bottles when the probability of successfully sampling 1 bottle is 0.25? (Hint: assume that the quietness of his actions guarantees the likelihood of success does not change between attempts).

A First Course in Probability (10th Edition)
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4. Jack's sister ordered 30 bottles of wine for her birthday party. A covid
lock-down caused her to cancel her (traditionally extravagant) party
this year and so she could not use the wine. Instead she decided to
store the wine in a spare room for 12 months and to use it next year.
Unfortunately, this wine is Jack's favourite. To ensure that the wine
is not spoiling in storage, Jack decides to quietly sample 5 bottles of
his sisters wine.
(a) How many possible ways can 5 bottles be chosen from a total of
30 if we do not care about the order in which they are chosen?
(b) Over the coming year, Jack attempts to quietly sample 1 bottle
per month. What is the probability that Jack samples exactly 5
bottles when the probability of successfully sampling 1 bottle is
0.25?
(Hint: assume that the quietness of his actions guarantees the
likelihood of success does not change between attempts).
Transcribed Image Text:4. Jack's sister ordered 30 bottles of wine for her birthday party. A covid lock-down caused her to cancel her (traditionally extravagant) party this year and so she could not use the wine. Instead she decided to store the wine in a spare room for 12 months and to use it next year. Unfortunately, this wine is Jack's favourite. To ensure that the wine is not spoiling in storage, Jack decides to quietly sample 5 bottles of his sisters wine. (a) How many possible ways can 5 bottles be chosen from a total of 30 if we do not care about the order in which they are chosen? (b) Over the coming year, Jack attempts to quietly sample 1 bottle per month. What is the probability that Jack samples exactly 5 bottles when the probability of successfully sampling 1 bottle is 0.25? (Hint: assume that the quietness of his actions guarantees the likelihood of success does not change between attempts).
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Given information:

Total no. of Wine bottles (n)=30Bottles to be selected (r)=5P(success)=0.25P(failure)=q=1-P(failure)=0.75

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