Aweighted die, numbered one through six, has a probability of 1/4 of rolling a six. if this die is rolled three times, and each roll is independent, what is the probability of rolling at least two sixes?

Step-by-step explanation:

Three events A, B and C are said to be independent if occurrence of one outcome does not affect the other .

In such case P ( A and B and C ) = P(A) × P(B) × P (C)

Given : A weighted die, numbered one through six, has a probability of 1/4 of rolling a six .

As the die is rolled three times, possible outcomes are

Let E denotes the event: 6 occurs

Let F denotes the event that 6 does not occur .

Given: P(E) =

So, P(F) =

Therefore, probability of rolling at least two sixes =

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0