# Probability

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"?

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

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)?

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

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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!

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2. welp

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