What is the difference between Conditional Probability and special rule of multiplication
i'm dealing wit the contingency table.
I........................ | Correct label | Incorrect label |
underweight ,U |...........68 ..... | ...........28..........|
Satisfactory, S | .........304.......| ...........59.........|
Overweight, O |..........24........ |..........17...........|
Find the probabilty of,
a bag of satisfactory weight is chosen, given it is correctly labeled.
My lecturer said it is conditional rule P (A | B) not multiplication rule P(A and B). WHY?
how u know when it is P (A | B) not P(A and B). i dunno how to differentiate. I cant see the difference.
How the question is when it is a conditional rule P (A | B) question.
Answer for tat question is 0.7677
2006-12-27 03:46:01 · 5 answers · asked by lim key earn 1 in Science & Mathematics ➔ Mathematics
The difference between conditional probability and the special rule of multiplication with probability is that conditional probability limits the sample space of the probability you are going to take.
In this problem, if you are solving for the probability of a bag of satisfactory weight with a correct label (i.e P(A and B)), then your sample space would be the entire table above with all the possible combinations. This would be equal to:
P(A and B) = 304/(68+304+24+28+59+17) = 0.608
Since you are given B, a correct label, you can limit your sample space to those with only correct labels. You can ignore the bags with incorrect labels because they do not belong in your sample space, due to the "given" portion. Therefore:
P(A given B) = 304/(68+304+24) = 0.7677
In general, when you see the word "given" in a probability problem, then you are dealing with conditional probability
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Hope this helps
2006-12-27 04:07:28 · answer #1 · answered by JSAM 5 · 1⤊ 0⤋
Conditional Probability Multiplication Rule
2016-11-04 05:24:40 · answer #2 · answered by ? 4 · 0⤊ 0⤋
Conditional probability limits the denominator (normallly reserved for the sample space) to the "given".
With the multiplication rule, you are simply figuring the probability of picking a bag that is correctly labelled, and then a bag of satisfactory weight. This would be the same as conditional probability if the bags of satisfactory weight were evenly distributed in the correctly labelled vs non correctly labelled bunch. Then A and B would be independant and conditional proablity would be the same as by the multiplication rule. But you can't always assume this, so you need to modify the definition of probability, which is
Probability of an event = (number of ways your event can happen) / (total number of events in the sample space)
You need to modify it to:
Conditional probability of an event = (number of ways your event can happen in the intersection of the event and the given) / (total number of events in the given)
Here, your numerator would be (number of bags of satisfactory weight in the subset of bags which were correctly labelled) and your denominator would be (number of bags correctly labelled.).
In other words, you are restricting the sample space to the bags which were correctly labelled, and you are restricting the event to those which are satisfactory weight AND correctly labelled.
Hope this helps.
The key word is "given". When you see this key word, you know that you will use conditional probability.
2006-12-27 03:50:14 · answer #3 · answered by Joni DaNerd 6 · 1⤊ 0⤋
She-nerd is right, although a bit brief. The key is the word "given." As soon as you see "given it is correctly labeled" you focus only on the first column. P(satisfactory | correctly labeled) = 304/396 = .767676....
When working with a table like this it is useful to compute row and column totals. 2nd row total is 363, so P(correctly labeled | label says satisfactory) = 304/363.
By contrast, P(label says satisfactory AND label is correct) = 304/500.
2006-12-27 04:07:02 · answer #4 · answered by Philo 7 · 1⤊ 0⤋
Conditional love is love given if someone "lives up to" an agreement of some kind with another. (ie. a guy wants sex with a girl, he'll only "love her" if she "puts out;" a woman wants a new "whatever" and will only "love" her partner if she gets what she wants, etc.). Conditional love is based on selfishness from the "receiver." Unconditional love is love given no matter what (ie. during hardship, anger, loss of money, whatever). It's based on concern/caring for another without anything expected in return.
2016-03-17 22:31:17 · answer #5 · answered by Anonymous · 0⤊ 0⤋