Question

A fair die is cast four times. Calculate

the probability of obtaining at least two
S6's.
Round to the nearest tenth of a
percent.

Answer 1

I'd say that is an "occupancy problem".

I ran a spreadsheet simulation of that and I'd say the probability is approximately .13

Those problems are rather complex to solve. What I think you would have to do is calculate the probability of

A) ZERO sixes appearing in 4 rolls.

B) exactly 1 six appears in 4 rolls.

C) exactly 2 sixes appear in 4 rolls.

D) exactly 3 sixes appear in 4 rolls. and

E) exactly 4 sixes appear in 4 rolls.

4 rolls of a die can produce 6^4 or 1,296 combinations.

A) is rather easy to calculate: The probability of NOT rolling a six in one roll is 5/6. In 4 rolls it would be (5/6)^4 = 0.4822530864

E) is fairly easy to calculate: The probability of rolling one six is (1/6). The probability of rolling 4 sixes is (1/6)^4 = 0.0007716049

Then we need to:

D) calculate how many ways can we place 3 objects into 4 bins

C) calculate how many ways can we place 2 objects into 4 bins

B) calculate how many ways can we place 1 objects into 4 bins

I don't know how to calculate D C and B

Explanation: