maths-probabilty

posted by .

Bag 1 contains 2 white and 3 red balls and bag 2 contains 4 white and 5 red balls. 1 ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag 2

  • maths-probabilty -

    The 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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. statistics

    Assume that each bag contains 6 balls. Bag a contains 3 red and 3 white, while bag b contains 2 red, 2 white, and 2 blue. You randomly select one ball from bag a, note the color, and place the ball in bag b. You then select a ball …
  2. FINITE

    selection of colored balls from two bags. Assume that each bag contains 4 balls. Bag a contains 2 red and 2 white, while bag b contains 2 red, 1 white, and 1 blue. You randomly select one ball from bag a, note the color, and place …
  3. Math

    A bag contains 5 red balls and 4 white balls. Two balls are drawn at random from the bag. The first ball drawn is put back into the bag before the second ball is drawn. What is the probability that two balls drawn are both red?
  4. Math

    A bag contains 5red balls and 4 white balls. Two balls are drawn at random from the bag. The first ball drawn is put back into the bag before the second ball is drawn. What is the probability that the two balls drawn are both red?
  5. maths-probabilty(URGENTLYYY)

    There are two bags out of which Bag 1 contains 2 white and 3 red balls and bag 2 contains 4 white and 5 red balls. 1 ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag …
  6. maths-probabilty

    There are two bags out of which Bag 1 contains 2 white and 3 red balls and bag 2 contains 4 white and 5 red balls. 1 ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag …
  7. maths- probabilty(me posted third time)plse answer

    There are two bags out of which Bag 1 contains 2 white and 3 red balls and bag 2 contains 4 white and 5 red balls. 1 ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag …
  8. elective mathematics

    A ba contains 5 red and 4 white identical balls abd a second bag contains 3 red and white identical balls If one ball ios selected at random from each of the bags, Find the probability that, two balls selected will be of I)different …
  9. Maths

    Bag A contains 2 white, 1 black and 3 red balls, Bag B contains 3 white, 2 black and 4 red balls and Bag C contains 4 white, 3 black and 2 red balls. One Bag is chosen at random and 2 balls are drawn at random from that Bag. Of the …
  10. Math

    A bag contains 5 red balls, 4 white balls, and 3 black balls. Two balls are drawn without replacement. What is the probability that at least one ball drawn is white?

More Similar Questions