Ques. a biased die has a probability of 1/4 of showing a 5, while the probability of any of 1, 2, 3, 4, or 6 turning up is the same . if three such dice are rolled, what is the probability of getting a sum of atleast 14 without getting a 6 on any die ?

Since the addition of every probable event is equal to 1 and the probability of rolling a five is 1/4, then the probability of any of the other numbers is:




Now, the condition is that no die rolls a six. Thus, we need to limit our sample space from 216 down to 125, to ensure we're not rolling a six.

The ways we can reach 14 or greater are:
5, 5, 5
4, 5, 5 (which can occur in 3 ways)

Thus, our probability becomes:

This question is incomplete, here is the complete question:

Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current revenues, they receive an additional $50,000,000 grant. This would allow them to reduce average tuition by how much?

A) $1388.89

B) $3571.43

C) $5555.56

D) $9500.00

E) $25888.89

number of students = 36,000

A) $

1388.89

Step-by-step explanation:

the college received additional grant which is $50,000,000

and the number of students is 36,000,

and we also know that expenses and enrollment remained the same.

So if we have more money (grants) and nothing changed (expenses remain the same)

dividing the grant by the number of students will show just how much the average tuition fee would be reduced

therefore R = G/n

R = 50,000,000 / 36000

R = 1,388.888 ≈  $1388.89