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anonymous

  • one year ago

A bag has 1 red marble, 4 blue marbles, and 3 green marbles. Peter draws a marble randomly from the bag, replaces it, and then draws another marble randomly. What is the probability of drawing 2 blue marbles in a row? Explain your answer.

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  1. Valpey
    • one year ago
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    Multiply the probability of drawing just one blue marble times itself.

  2. anonymous
    • one year ago
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    wait. So 1*4?

  3. Valpey
    • one year ago
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    The probability of drawing one blue marble is equal to the fraction: number of blue marbles over the total number of marbles.

  4. Valpey
    • one year ago
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    Which is more likely, drawing a blue marble or flipping a coin and getting tails?

  5. anonymous
    • one year ago
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    drawing a blue marble i am assuming because there is only one side that has tails when there are four different blue marbles.

  6. anonymous
    • one year ago
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    what am multiplying exactly though besides the one marble? The mean times the one marble? the fraction would be 4/8 or simplified to 1/2

  7. anonymous
    • one year ago
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    @Valpey @Hero

  8. Valpey
    • one year ago
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    Right 1/2 or 50% of the time you draw a blue marble.

  9. Valpey
    • one year ago
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    What percent of the time do you draw a blue marble twice in a row? (same as getting tails in two coin tosses)

  10. anonymous
    • one year ago
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    thats the part I am confused about.

  11. Valpey
    • one year ago
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    If I flip a coin twice, what is the chance it comes tails, tails?

  12. anonymous
    • one year ago
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    it could be HH TT or TH. so I would say 1/3 or a chance...

  13. anonymous
    • one year ago
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    of*

  14. anonymous
    • one year ago
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    I am so confused @Valpey

  15. Valpey
    • one year ago
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    You left out HT which is just as likely as TH. So the four equally likely outcomes are: HH, TH, HT, TT Similarly let's say B for Blue Marble and N for Not Blue Marble. The four equally likely outcomes are: BB, BN, NB, NN

  16. anonymous
    • one year ago
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    ohhhhhh okay

  17. anonymous
    • one year ago
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    But how does that go along with the problem? hehe sorry im slow

  18. anonymous
    • one year ago
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    @Valpey

  19. Valpey
    • one year ago
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    The answers are the same. Blue marbles represent 50% of the marbles so drawing one is equivalent to any other 50:50 outcome, like tossing a coin.

  20. Valpey
    • one year ago
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    The chance of drawing two Blue Marbles in a row (with replacement) is the same as the chance of flipping a coin twice and getting tails, tails. This happens 1 in 4 times or 25%.

  21. Valpey
    • one year ago
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    But we can change the problem slightly and see better how to extend this. Suppose instead there are 3 Blue Marbles and 5 Not Blue Marbles. Now we still have four possible outcomes: BB, BN, NB, NN but now they are not all equally likely. Each outcome is the product of the chance of the two independent events separately. BB = \(\frac{3}{8}*\frac{3}{8} =\frac{9}{64}\) BN = \(\frac{3}{8}*\frac{5}{8} =\frac{15}{64}\) NB = \(\frac{5}{8}*\frac{3}{8} =\frac{15}{64}\) NN = \(\frac{5}{8}*\frac{5}{8} =\frac{25}{64}\)

  22. anonymous
    • one year ago
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    OHHHHHhhhhhhhhhhhHHHHHHHHhhhhhhhHHHHHHHhhhH

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