Let’s say you have an unfair six-sided die that lands on 2 exactly 20% of the...

Let’s say you have an unfair six-sided die that lands on 2 exactly 20% of the time. If you roll this “loaded” die 5 times, what are the odds that you: (a) never roll a 2, (b) roll a 2 two times, or (c) roll a 2 more than two times? (use excel and show functions)

Solutions

Expert Solution

Probability that the die lands on 2 = 20% = 0.2

The die is rolled 5 times.

Let X be the number of times the die lands on 2 among the 5 times it is rolled.

Thus clearly X ~ Binomial(5,0.2)

Odds that you never roll a 2 = P(X=0)/[1- P(X=0)] = 0.487387

[ The above value is obtained by using the function =BINOMDIST(0,5,0.2,FALSE)/(1-BINOMDIST(0,5,0.2,FALSE)) in Excel 07. ]

Odds ratio that you roll a 2 two times = P(X=2)/[1- P(X=2)] = 0.257545

[ The above value is obtained by using the function =BINOMDIST(2,5,0.2,FALSE)/(1-BINOMDIST(2,5,0.2,FALSE)) in Excel 07. ]

Odds ratio that you roll a 2 more than two times = P(X>2)/[1- P(X>2)] = [1-P(X2)]/P(X2) = 0.061481

[ The above value is obtained by using the function =(1-BINOMDIST(2,5,0.2,TRUE))/BINOMDIST(2,5,0.2,TRUE) in Excel 07. ]

milcah answered 10 months ago

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