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# Introductory Statistics??? watch

1. P[A'] = 0.4 , P[B] = 0.3 and P[A|B] = 0.5

This is all the information given to me and I have to find
a. Are events A and B mutually exclusive?
b. Are events A and B statistically independent?
c. Find P[AUB]
d. Find P[B|A] + P[A|B]
e. Is event/set B a subset of event/set A?

My professor is terrible at explaining things and I am so lost. Help would be greatly appreciated!
2. (Original post by tundrawolf)
P[A'] = 0.4 , P[B] = 0.3 and P[A|B] = 0.5

This is all the information given to me and I have to find
a. Are events A and B mutually exclusive?
b. Are events A and B statistically independent?
c. Find P[AUB]
d. Find P[B|A] + P[A|B]
e. Is event/set B a subset of event/set A?

My professor is terrible at explaining things and I am so lost. Help would be greatly appreciated!
This is an exercise in manipulating definitions and in understanding what the definitions mean. Let's see if we can get you started:

You've been given and . From these you can work out and , the latter using the formula that defines . Then,

(a) Two events are mutually exclusive if they never happen together. Can you express that in terms of things we've already got to hand?
(b) The two events are independent if . You already have the information to work this out.
(c) There's a formula relating to

If you get this far, you should be well set for the rest of the question!
3. (Original post by Gregorius)
This is an exercise in manipulating definitions and in understanding what the definitions mean. Let's see if we can get you started:

You've been given and . From these you can work out and , the latter using the formula that defines . Then,

(a) Two events are mutually exclusive if they never happen together. Can you express that in terms of things we've already got to hand?
(b) The two events are independent if . You already have the information to work this out.
(c) There's a formula relating to

If you get this far, you should be well set for the rest of the question!
Okay so for P[A] I got 0.6.

For part a I got they are mutually exclusive, but I totally guessed because I never got a straight definition of that

For part b I got them as being not statistically independent by doing P[A|B] = P[B] which is 0.5 = 0.6 which doesn't work so

For part c I did P[AUB] = P[A] + P[B] since I got that they are mutually exclusive. With that I did 0.6 + 0.3 getting 0.9 as an answer.

For part d I had to find P[B|A] = P[A intersect B] / P[A] and for that answer I got 0.15/0.3 which equals 0.25. Then I added 0.25 and 0.5 together getting 0.75. I don't think I did that right and none of my notes explain any of this so I just winged it... Help would be greatly appreciated on this part

For part e I literally just guessed yes.
4. (Original post by tundrawolf)

For part a I got they are mutually exclusive, but I totally guessed because I never got a straight definition of that
Two events are mutually exclusive if they never occur together. In other words . Now, you can work out from what you have...
5. So to find P[A intersect B] I have to do P[A|B] * P[B] right? Which is 0.15. So they aren't mutually exclusive?

I apologize for all the questions, my professor doesn't make any sense.
6. (Original post by tundrawolf)
So to find P[A intersect B] I have to do P[A|B] * P[B] right? Which is 0.15. So they aren't mutually exclusive?
You've got it.

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