1. We roll a fair five-sided die with numbers from 1 to 5. Assume observing 4 or 5 is success. Random variable of interest is the number of successes when we roll the die 10 times. a. What is the chance of having exactly one success (observing 4 or 5)? b. Find the expected number of successes. c What is the standard deviation of number of successes?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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1. We roll a fair five-sided die with numbers from 1 to 5. Assume observing 4 or 5 is success.
Random variable of interest is the number of successes when we roll the die 10 times.
a. What is the chance of having exactly one success (observing 4 or 5)?
b. Find the expected number of successes.
c. What is the standard deviation of number of successes?
d. How many times we must roll the die to have 6 successes in average?
Transcribed Image Text:1. We roll a fair five-sided die with numbers from 1 to 5. Assume observing 4 or 5 is success. Random variable of interest is the number of successes when we roll the die 10 times. a. What is the chance of having exactly one success (observing 4 or 5)? b. Find the expected number of successes. c. What is the standard deviation of number of successes? d. How many times we must roll the die to have 6 successes in average?
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