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).

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)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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