Condtional Probability, Multiplication Rule: cola drinkers

peggyskold said:

Can someone please help me to understand this rule for dependent events P(A) P(A/B) what are the math operations to do this? I know I am just missing something here but I need to grasp how to do this.
P(B/A) I know it is is supposed to be P(B) the probability of event B - given that A has happened, P(A) the probability of event a and then what do you to to figure out P(B/A) ? Is this event B divided by event A? NO....don't get it.
for instance I can do this type (I think)

Code:

              Water   Orange juice      Cola
Under 21 years	40      25	           20
21 – 40 years	 35      20	           30
Over 40 years	 20      30	           35

If one of the 255 subjects is randomly chosen, find the probability that the person drinks cola given they are under 21.

Total number of under 21 = 40 + 25 + 20 = 85

So probability of choosing somebody under 21 = 85/255 = P(A) = 1/3

Given under 21, probability s/he drinks cola = P(B/A) = 20/85

So probability that somebody is under 21 AND drinks cola = 1/3 * 20/85 = 4/51


So the total number of those who drink cola is 85 and the total number of those who are under 21 is 20. So I divide 20/85 to get 0.235. (I think this is right)

On this one, even though I am looking at the solution of this one I can't quite understand it;
In the general populaton one woman in eight will develop breast cancer. Research shows that 1 woman in 600 carries a BRCA gene. Eight out of 10 women with this mutation develop breast cancer.

Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene.
The solution is P(B) = 1/8, P(A) = 1/600, and P(B/A) = 8/10. So P(B/A)=8/10 = 0.8

However, the statement of the problem is little bit convoluted.

What operations did they do to get the 8/10?

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Water Orange juice Cola
Under 21 years 40 25 20
21 – 40 years 35 20 30
Over 40 years 20 30 35

If one of the 255 subjects is randomly chosen, find the probability that the person drinks cola given they are under 21.

So the total number of those who drink cola is 85 and the total number of those who are under 21 is 20. So I divide 20/85 to get 0.235. (I think this is right)

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Your answer is correct – but only by unfortunate coincidence. Please read carefully what Subhotosh has provided. The confusion occurs because both the “cola column” and the “under 21 row” happen to total 85.

When you have a “given condition” – in this case it’s “under 21” – focus only on that row or column.

Your problem, P(drinks cola | under 21) = 20/(40+25+20) = .235wjm11

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