SOLUTION: If we roll a die two times, determine whether the following pairs of events are independent or dependent? a. Event A is rolling a 4 on the first die. Event B is rolling a 5 on t

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Question 1168716: If we roll a die two times, determine whether the following pairs of events are independent or dependent?
a. Event A is rolling a 4 on the first die. Event B is rolling a 5 on the second die.
b. Event A is rolling a 3 on the first die. Event B is getting the sum of more than 6 with the two dice.
Found 2 solutions by solver91311, Boreal:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Ask yourself, does the outcome of event B depend in any way on the outcome of event A? That is to say, is the probability of B changed in any way by whether or not event A occurs?

If B "depends" on A, then they are dependent events otherwise they are independent events. Hence the names.

John

My calculator said it, I believe it, that settles it

I > Ø

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
These are independent probability of each is (1/6), probability of both is 1/36. Also, what happens on first roll has no bearing upon the second roll.

The second isn't clear. If a is one roll and b is a different roll with BOTH die, then they are independent.
If, however, a is the first roll, then b is a roll of the other die, and the two are added, then this is a dependent case, since the roll in the first case has direct bearing upon the sum in the second case. If it is a 3, then the second die need to be 4,5,6. If the first were a 1, then the second would have to be a 6.
(1/6)(1/2)=(1/3), since the second die has to be 4,5,6.
separately, they are (1/6) and (21/36) or (7/12), and that product is 7/72.