Probability and Statistics homework

Hey guys, I am trying to figure out these two problems, but I cann't really understand what my teacher is asking for. Could someone please help? Its do tomorrow.

1) For events A and B, find the formulas for the probabilities of the following events in terms of quantities P(A), P(B), and P(AnB). (n denotes intersection, and u denotes union)

A) either A or B or both
B) either A or B but not both
C) at least one of A or B
D) At most one of A or B

My answers: (my answers may be so wrong, the teacher didn't even explain this)
A) P(A)uP(B)
B) P(AnB)
C) P(A)
D) P(B)

2) A) In a draft lottery containing the 366 days of the year (including Feb. 29), what is the probability that the first 180 days drawn(without replacement) are evenly distributed among the 12 months?

B) What is the probability that the first 30 days drawn contain none from September?

Hi !

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Originally Posted by Dream

Hey guys, I am trying to figure out these two problems, but I cann't really understand what my teacher is asking for. Could someone please help? Its do tomorrow.

1) For events A and B, find the formulas for the probabilities of the following events in terms of quantities P(A), P(B), and P(AnB). (n denotes intersection, and u denotes union)

A) either A or B or both
B) either A or B but not both
C) at least one of A or B
D) At most one of A or B

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A) P(A)uP(B)

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Ouch !
u is used for sets, not for numbers such as P(A) and P(B)
"either A or B or both" is equivalent to A u B
But in general, P(A u B)=P(A)+P(B)-P(A n B) (see a Venn diagram for understanding)

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B) P(AnB)

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No, what you wrote is "A and B"

either A or B but not both : please look at the sketch.

Attachment 7692

You want the grey and the blue parts and only them.
See what its complement is : orange and green parts --> (A u B)' u (A n B)=(A' n B') u (A n B)

So either A or B but not both is : [(A u B)' u (A n B)]'
Good luck :D

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C) P(A)
D) P(B)

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Did you answer them randomly ? o.O

C) You want at least one of A or B. This is A u B.

D) At most one of A or B is the complement of "A and B" (try to think why), that is (A n B)'

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2) A) In a draft lottery containing the 366 days of the year (including Feb. 29), what is the probability that the first 180 days drawn(without replacement) are evenly distributed among the 12 months?

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So 15 days per month.
Apply this : Hypergeometric distribution - Wikipedia, the free encyclopedia (multivariate hypergeometric distribution) to your question

-------- for this question, I'm not sure... hey, why wouldn't you tell me what's your idea ? :D ---------

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B) What is the probability that the first 30 days drawn contain none from September?

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September contains 30 days.
Apply the hypergeometric distribution (link above), considering :
- group A : every day of september (30)
- group B : every day not in september (336)


(Whew)

Nope, my teach is really this horrible. Sometimes I wonder why I go to class. Thank you for the help.