If a single sixsided die is rolled five times, what is the probability that a six is thrown exactly three times?







Answer is b) 0.032
We are given that a six sided die is rolled five times .
So here number of trials are 5 , n = 5
Probability of getting a six on a single trial = 1/ 6 ( Since if a die rolled , there are 6 possible outcomes 1,2,3,4,5,6 , so probability of getting 6 is 1/6 )
Now we are asked to find probability that a six is thrown exactly three times .
Let x be the random variable represents the number of times a six is thrown.
Therfore x follows binomial distribution with probability p = 1/6 and trials n = 5
We have to calculate P( x = 5 ) using binomial formula
P( X =x ) = ; x = 0,1,2,3....n.
You can use excel function =BINOMDIST( x,n,p,cumulative ) to find this binomial probability for n = 5 , p = 1/6 and x =5 .( for cumulatuve use FALSE )
=BINOMDIST(3,5,1/6,FALSE)
=0.032
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