Friday

September 19, 2014

September 19, 2014

Posted by **anoynomous** on Wednesday, March 20, 2013 at 1:07pm.

- maths-probabilty -
**Count Iblis**, Wednesday, March 20, 2013 at 2:05pmThe probabilities for drawing a red ball from a particular bag are:

P(red|bag1) = 3/5

P(red|bag2) = 5/9

The conditional probability that a variable X takes some value given that another variable Y takes some value, denoted as P(X|Y) is related to the joint probability as follows:

P(X,Y) = P(Y)*P(X|Y)

So, in P(X|Y) it is given that Y takes some vale and then you can consider the probability as a function of X given that Y has that known value. If you multiply that by the probability that Y has this value in the first place,

P(Y), then you get the joint probability P(X,Y).

In this case, each bag has a prior probability of 1/2, so the joint probability for drawing a red ball and having chosen a particular bag are:

P(red, bag1) = 1/2 * 3/5 = 3/10

P(red, bag2) = 1/2 * 5/9 = 5/18

Then to find the conditional probabilities for the ball coming from a particular bag, given that the ball was red, you need to divide the joint probabilities by the prior probability for the ball being red, P(red.

We can obtain P(red) from summing the joint probabilities over all the bags:

P(red) = P(red, bag1) + P(red, bag2) =

3/10 + 5/18 = 26/45

Therefore:

P(bag1|red) = P(red, bag1)/P(red) =

27/52

P(bag2|red) = P(red, bag2)/P(red) =

25/52

**Answer this Question**

**Related Questions**

maths- probabilty(me posted third time)plse answer - There are two bags out of ...

maths-probabilty(URGENTLYYY) - There are two bags out of which Bag 1 contains 2 ...

maths-probabilty - There are two bags out of which Bag 1 contains 2 white and 3 ...

Maths - Bag A contains 2 white, 1 black and 3 red balls, Bag B contains 3 white...

FINITE - selection of colored balls from two bags. Assume that each bag contains...

statistics - Assume that each bag contains 6 balls. Bag a contains 3 red and 3 ...

Math - A bag contains 5 red balls and 4 white balls. Two balls are drawn at ...

Math - A bag contains 5red balls and 4 white balls. Two balls are drawn at ...

MATH 12 HELP! - One bag contains 4 white balls and 6 black balls. Another bag ...

******MATH 12******* - How about this. One bad contains 4 white balls and 6 ...