Probability - Dependent events

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ssb

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Hey guys,

so I started the unit on independent and dependent events in probability.

probability-independent-formula2.gif


I'm having problems defining the A and B in problems.

for example

Find the probability of rolling a sum greater than 7 with two dice if it is known that the first dice rolled is a 3?

we can easily state:
let A represent a sum greater than 7
let B represent the first die being 3
... Then from here we can solve problems


SO my question is how do you guys identify the two variables? What are some clues? What helps you?Please share any helpful tips. Thanks.
 
ssb said:
probability-independent-formula2.gif


I'm having problems defining the A and B in problems. For example:

Find the probability of rolling a sum greater than 7 with two dice if it is known that the first dice rolled is a 3?
Click to expand...
On the left-hand side of the equation in the graphic, you have an expression which means "the probability P of B, given A". So you'd probably want to assign the "A" variable to the "given" (that is, what you're supposed to assume, or else what is already known). Then assign the "B" variable to what you're needing to find. ;)
 
ssb said:
Find the probability of rolling a sum greater than 7 with two dice if it is known that the first dice rolled is a 3 SO my question is how do you guys identify the two variables? What are some clues? What helps you?Please share any helpful tips.
Click to expand...

You have asked an almost unanswerable question.
Look at your example: "rolling a sum greater than 7 with two dice if it is known that the first die rolled is a 3" (pleae note the singular form).
The given is "first die rolled is a 3", so that defines a subspace of six. In that new space there are only six pairs of which only one has a sum pf six. So the question is trivial.

On the other hand, if the question were: "Find the probability of the first dice rolled is a 3 if it is known that rolling a sum greater than 7 with two dice." Now that is an interesting question.
 
stapel said:
On the left-hand side of the equation in the graphic, you have an expression which means "the probability P of B, given A". So you'd probably want to assign the "A" variable to the "given" (that is, what you're supposed to assume, or else what is already known). Then assign the "B" variable to what you're needing to find. ;)
Click to expand...

Ah. This makes much more sense. Can I apply this to any given question? sometimes it can be hard to identify what is given by the way the question is written but yeah.hahah
 
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