Hi,

The probability of rolling exactly three 4's in 5 rolls of a fair  die

P(rolling a four)= 1/6

P(not rolling a four) = 5/6

 1/6*1/6*1/6*5/6*5/6

distinguishable orders of the five rolls/3fours and '2' others:5!/[3!*2!]=10

P(exactly 3 fours in five rolls) = 10*(1/6*1/6*1/6*5/6*5/6) 

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
 The probability of rolling exactly three 4's in 5 rolls of a fair die

---

Binomial Problem with n = 5 and p = 1/6

---

P(x = 3) = 5C3(1/6)^3(5/6)^2 = 10*(25/6^5) = 0.0322

==================

Cheers,

Stan H.

========= 

Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
 p=probability of rolling a four

p=1/6, q=5/6

(p+q)^5 expand

5C3=10 coefficient

10p^3q^2=.03215 third term of the expansion.

.

Ed 

RELATED QUESTIONS

find the probability of obtaining exactly two 5's in six rolls of a fair... (answered by jorel1380)

Find the probability of rolling 3 successive 2's with 3 rolls of a fair... (answered by oberobic)

What is the probability of rolling a 3 on two consecutive rolls of a fair die?  (answered by Tatiana_Stebko)

Find the probability of three consecutive 2's turning up in rolling a fair die three... (answered by ikleyn)

A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly  (answered by reviewermath)

an experiment consists of rolling a fair die three times, what is the probability of... (answered by stanbon)

an experiment consists of rolling a fair die three times, what is the probability of... (answered by stanbon)

You toss a fair 6-sided die 5 times.find the probability that a three is rolled exactly... (answered by ewatrrr,edjones)

What is the probability that 6 rolls of a fair die will show four exactly 5... (answered by Edwin McCravy)