This is my second class in intro to probability at a university level.

1) There are 5 people in a room with 3 boys and 2 girls. If I randomly pick 1 person from the box, P(boy)=3/5. If I randomly pick 2 people, P(pick 2 girls) = 2/5 x 1/4 = 1/10.

a) Now what is P(pick 1 girl and 1 boy) equal to if the order doesn't matter?

b) What is P(pick 1 girl and 1 boy) equal to if the order does matter?
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1a) My guess is that P(pick 1 girl and 1 boy) = 2/5 x 3/4 = 6/20 = 3/10 if the order doesn't matter. Is this right?

1b) No idea...

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2) What is the difference between an "independent event" and a "mutually exclusive event"? I can't visualize the difference...


Can someone help me please?

The second question first.
Mutually exclusive events are events that can't happen together.
If A and B are mutually exclusive, then P(A|B)=0 and P(B|A)=0

For a roll of two dice, for example, the two events (first die shows 2) and (total is 10) are mutually exclusive. They can't both happen.

Independent events are events that have no bearing on each other. If you know whether one event has happened, it doesn't give you any information about whether the other happened or not. If A and B are independent, P(A|B)=P(A) and P(B|A)=P(B).

For a roll of two dice, the events (first die shows 6) and (second die shows 6) are independent. The one doesn't change the likelihood of the other.

1) There are 5 people in a room with 3 boys and 2 girls. If I randomly pick 1 person from the box, P(boy)=3/5. If I randomly pick 2 people, P(pick 2 girls) = 2/5 x 1/4 = 1/10.

a) Now what is P(pick 1 girl and 1 boy) equal to if the order doesn't matter?

b) What is P(pick 1 girl and 1 boy) equal to if the order does matter?
=====================
1a) My guess is that P(pick 1 girl and 1 boy) = 2/5 x 3/4 = 6/20 = 3/10 if the order doesn't matter. Is this right?
P(girl first, then boy) = 2/5 x 3/4
P(boy first, then girl) = 3/5 x 2/4
Add the two together to get the answer for 1a).

2) Thanks for the great explanation. It's really helpful!

But I think you mean
"Independent events are events that DON'T have any bearing on each other"
right?

P(girl first, then boy) = 2/5 x 3/4
P(boy first, then girl) = 3/5 x 2/4
Add the two together to get the answer for 1a).

Why do I have to add the two together? Is there a theorem supporting this?

Event1: girl first, then boy
Event2: boy first, then girl
By the way, are these 2 events an example of mutally exclusive events?

But I think you mean
"Independent events are events that DON'T have any bearing on each other"
right?

Yes. :o
Fixed now.

Why do I have to add the two together? Is there a theorem supporting this?
Ummm - I think so... I think it looks like this:
P(A or B) = P(A) + P(B) - P(A and B)

Event1: girl first, then boy
Event2: boy first, then girl
By the way, are these 2 events an example of mutally exclusive events?
Yes. So P(A and B) = 0.