Hailey plans to buy some items from the concession stand at the movie theater. The prices listed in the chart do not include tax
1 answer:
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Answer:
a)
And if we solve for P(M) we got:
And replacing we got:
b) In order to A and M be mutually exclusive we need to satisfy:
And for this case since the events A and M are NOT mutually exclusive
c) In order to satisfy independence we need to have the following relation:
And for this case we have that:
So then A and M are NOT independent
d)
And we can use the Bayes theorem and we got:
And replacing we got:
e)
And we can use the Bayes theorem and we got:
And replacing we got:
Step-by-step explanation:
For this case we define the following events:
A denote the event of receiving an Athletic Scholarship.
M denote the event of receiving a Merit scholarship.
For this case we have the following probabilities given:
Part a
For this case we can use the total rule of probability and we have this:
And if we solve for P(M) we got:
And replacing we got:
Part b
In order to A and M be mutually exclusive we need to satisfy:
And for this case since the events A and M are NOT mutually exclusive
Part c
In order to satisfy independence we need to have the following relation:
And for this case we have that:
So then A and M are NOT independent
Part d
For this case we want this probability:
And we can use the Bayes theorem and we got:
And replacing we got:
Part e
For this case we want this probability:
And we can use the Bayes theorem and we got:
And replacing we got: