Question

You roll two five-sided dice. The sides of each die are numbered from 1 to 5. The dice are “fair" (all sides are equally likely), and the two die rolls are independent.

Part (a): Event A is “the total is 10" (i.e., the sum of the results of the two die rolls is 10).

Is event A independent of the event “at least one of the dice resulted in a 5"?

- unanswered

Is event A independent of the event “at least one of the dice resulted in a 1"?

- unanswered

Part (b): Event B is “the total is 8."

Is event B independent of getting “doubles" (i.e., both dice resulting in the same number)?

- unanswered

Given that the total was 8, what is the probability that at least one of the dice resulted in a 3?

Answer 1

part (a)
1 and 2 No.

part (b)
1. No.

2. Looks like conditional probability (i failed this question. This answer was not used back in the day)

scenarios:
(the only possibility for an 8)


3,5 =0.2*0.2
4,4=0.2*0.2
5,3=0.2*0.2

at least one of the dices was a 3?
So thus = 0.08/0.12 =0.66666667

hope it helps!