A fair die is cast seven times. Calculate the probability of obtaining exactly three 6's. Round the answer to the nearest thousandth.
A) 0.076
B) 0.069
C) 0.078
D) 0.083
E) 0.082

Question

Quizplus · Accepted Answer

The probability of getting a 6 on any one throw is 1/6. 
The probability of not getting a 6 on any one throw is 5/6. 
Using the binomial distribution formula, the probability of getting exactly three 6's is: 
C(7,3) * (1/6)^3 * (5/6)^4 = 35/2592 ≈ 0.0135 ≈ 0.078 (rounded to the nearest thousandth).
Therefore, the answer is Choice C.

A Fair Die Is Cast Seven Times