You roll a fair die three times. what is the probability of each of the following?
a) you roll all 4's.
b) you roll all even numbers.
c) none of your rolls gets a number divisible by 2.
d) you roll at least one 2.
e) the numbers you roll are not all 2's.

(a)

(b)

(c)

(d)

(e)

Step-by-step explanation:

It is given that we roll a fair die three times. We need to find the following probability.

Total possible value = 1,2,3,4,5,6

(a) You roll all 4's.

Probability of getting a 4 =

Probability of getting 4 on all rolls =

Therefore, the probability of getting 4 on all rolls is .

(b) You roll all even numbers.

Even number = 2,4,6

Probability of getting an even number

Probability of getting even number on all rolls =

Therefore, the probability of getting even number on all rolls is .

(c) None of your rolls gets a number divisible by 2.

odd number = 1,3,5

Probability of getting an odd number

Probability of getting odd number on all rolls =

Therefore, the probability of getting odd number on all rolls is .

(d) You roll at least one 2.

Probability of getting a 2 =

Probability of getting any number except 2 =

Probability of getting any number except 2 in all rolls =

Probability of getting at least one 2 = 1 - P(getting no 2)

Probability of getting at least one 2 =

Therefore, the probability of getting at least one 2 is .

(e) The numbers you roll are not all 2's.

Probability of getting a 2 =

Probability of getting all 2 =

Probability of getting all not all 2's =

Therefore, the probability of getting not all 2's is .

6 on both sides and twelve on the top and the bottom

step-by-step explanation: