Question

If a die is rolled 35 times, there are 6 different sequences possible. The following question asks how many of these sequences satisfy certain conditions. HINT (Use the decision algorithm discussed in Example 3 of Section 6.3.] What fraction of these sequences have exactly five 1s? (Round your answer to four decimal places.) X sequences Need Help? Read It Take Tutor

Answer 1

We have rolled die 35 times.In those 35 rolls we want there to be exactly five 1's.

We could roll a 1 on each of the 5 rolls and the none more.

Or you could roll a 1 on the first four,then on sixth,then none more.

Or you could roll a 1 on the first four,then on seventh,then none more.

Or you could roll a 1 on first four,then on eighth,then none more....

So the problem really becomes how many different way can you arrange 5 occurences of an event(roll a 1) out of 35 events(35 rolls of the die)

We can apply binomial formula C(n,x)p^x(1-p)^n-x

Here n=35 , x=5 , p=1/6

C(35,5)(1/6)^5(1-1/6)^30

=324632×(1/7776)×4.21

=175.76