has anyone taken a probability course?

[skim milk]

I'm having problems understanding this question


A pair of fair dice is rolled. Let A denote the event that the sum of the dice is equal to 7.
a) show that A is independent of the event that the first die lands on 4
b) show that A is independent of the event that the second die lands on 3

I'm not sure how to show A is independent

 

[BigJ]

http://people.hofstra.edu/Stef...ialsf3/frames6_5C.html

 

[sao123]

Originally posted by: fritolays
I'm having problems understanding this question


A pair of fair dice is rolled. Let A denote the event that the sum of the dice is equal to 7.
a) show that A is independent of the event that the first die lands on 4
b) show that A is independent of the event that the second die lands on 3

I'm not sure how to show A is independent

unoficially...

if the first die is 4... then there is 1/6 chance of rolling 7.
if the first die is 3... then there is 1/6 chance of rolling 7.


there are 36 possible combinations, 6 of them roll 7
1,6
6,1
2,5
5,2
3,4
4,3

6 out of 36 is still 1/6

so 1/6 = 1/6 its independent.

 

[Kelemvor]

Sounds good to me.

 

[alkemyst]

This question has come up a few times here. It really depends on how the question is worded.

 

[MaxDepth]

Maybe...

What do you think my chances were?

EDIT: Okay, smart-ass answer aside. The word independent is to denote the act itself. Truly there is no causality between one event and the next.

If I flip a penny 50 times and each time it comes up heads, it is not impossible, just improbable. And the 51st coin toss is an event in and of itself. There are two probable outcomes (if you were to ignore the possibility of it landing on its edge). The event is still 1 of 2.


So in your dice question, even though the outcome is seven and one die is 4, then the event still has one/sixth of a chance of it being a three. And the two dice do not work together to create a seven, each is independent of the other.

Unless of course you throw two dice together and they collide.

 

[TuxDave]

Calculate the Probability of A
Calculate the Probability of A given the other Event (conditional probability)

If they are equal, they are independent.
P(A|B) = P(A) is true for independent events A and B.

 

[Fritzo]

The chances of me having taken a probablity class are 42.3423:1 against.