Answer:
a)
And if we solve for we got:
b) False
The reason is because we don't satisfy the following relationship:
We have that:
c) False
In order to satisfy independence we need to have the following condition:
And for this case we don't satisfy this relation since:
Step-by-step explanation:
For this case we have the following probabilities given:
Part a
We want to calculate the following probability:
And we can use the total probability rule given by:
And if we solve for we got:
Part b
False
The reason is because we don't satisfy the following relationship:
We have that:
Part c
False
In order to satisfy independence we need to have the following condition:
And for this case we don't satisfy this relation since: