Question

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

a)

0.125

b)

0.032

c)

0.042

d)

0.5

Answer 1

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