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Anita505 Group Title

Suppose that we have a white urn containing four white balls and one red ball and have a red urn containing one white ball and four red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) Selecting at random a ball from the urn having the colour of the first ball. Find the probability that the second ball is red. The probability that the second ball is red is ______.

  • one year ago
  • one year ago

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  1. kropot72 Group Title
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    There are two situations to consider: (1) If a white ball is selected on the first draw then the second draw will be from the white urn. Probability of white on the first draw is 4/5 and the probability of red on the second draw is 1/4. P(red second ball) = 4/5 * 1/4 = 4/20 ...............(1) (2) If a red ball is selected on the first draw then the second draw will be from the red urn. Probability of red on the first draw is 1/5 and the probability of red on the second draw is 4/5. P(red second ball) = 1/5 * 4/5 = 4/25 ...............(2) The probability that the second ball is red is the sum of the fractions (1) and (2).

    • one year ago
  2. Anita505 Group Title
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    so the sum of (4/20)+(4/25) So in this case the answer would be 0.36 correct?

    • one year ago
  3. kropot72 Group Title
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    Correct, or alternatively 9/25.

    • one year ago
  4. Anita505 Group Title
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    thank you for showing me the process

    • one year ago
  5. kropot72 Group Title
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    You're welcome :)

    • one year ago
  6. Anita505 Group Title
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    An urn contains 3 one-dollar bills, 1 five- dollar bill and 1 ten dollar bill. A player draws bills one at a time without replacement from the urn until a ten dollar bill is drawn. Then the game stops. All bills are kept by the player. Determine: A) The probability of winning $15 B)The probability of winning all bills in the urn C) The probability of the game stopping at the second draw.

    • one year ago
  7. Anita505 Group Title
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    can you help me with this and show me the process?

    • one year ago
  8. satellite73 Group Title
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    as far as i can see there is only one way to win $15: first draw the five, then draw the ten

    • one year ago
  9. satellite73 Group Title
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    since there are 5 bills, and one is a five, the probability of drawing the five first is \(\frac{1}{5}\) then there are 4 bills of which one is a ten, the probability of drawing a ten second given that the first bill was a five is \(\frac{1}{4}\) the probability of both things occurring is \[\frac{1}{5}\times \frac{1}{4}\]

    • one year ago
  10. Anita505 Group Title
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    so for part a) it would be 1/20? the answer

    • one year ago
  11. satellite73 Group Title
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    yes

    • one year ago
  12. Anita505 Group Title
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    okay thank you but i need help with part b and c

    • one year ago
  13. satellite73 Group Title
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    for b) it means you pick the ten dollar bill last right?

    • one year ago
  14. satellite73 Group Title
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    the probability you pick the ten dollar bill last is the same as the probability you pick the ten dollar bill first, namely \(\frac{1}{5}\)

    • one year ago
  15. Anita505 Group Title
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    so b then in this case is 1/5

    • one year ago
  16. satellite73 Group Title
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    and for the last one, that means you pick something other then the ten dollar bill, and then you pick the ten dollar bill that is also \(\frac{1}{5}\) via \[\frac{4}{5}\times \frac{1}{4}=\frac{1}{5}\]

    • one year ago
  17. satellite73 Group Title
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    more simply put, the probability you pick the ten first, second, third, fourth or fifth are all the same, namely \(\frac{1}{5}\)

    • one year ago
  18. Anita505 Group Title
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    Okay thank you for your assistance i have one last question to ask,

    • one year ago
  19. satellite73 Group Title
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    do me a favor and post in a new thread this is hard so scroll down to

    • one year ago
  20. Anita505 Group Title
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    A grade 11 art class is offering students two choices for a project: a pottery project and a mixed media project. Of the 46 students in the class, 23 have selected to do the pottery project and 33 have selected to do the mixed media project (notice some students have decided to do both) It two students are selected at random from the class to show their finished project(s), what is the probability that at least one pottery project and at least one mixed media project will be shown? Probability (given to three decimal places)

    • one year ago
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