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Pulsified333

  • one year ago

involving the sum of the numbers showing on two fair dice. (1) What is the probability that exactly one die shows a 6 given that the sum of the numbers is 9? (2) What is the probability that the sum of the numbers is 9 given that exactly one die shows a 6? (3) What is the probability that the sum of the numbers is 9 given that at least one die shows a 6?

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  1. Pulsified333
    • one year ago
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    @jim_thompson5910

  2. jim_thompson5910
    • one year ago
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    which one are you stuck on? how far did you get?

  3. Pulsified333
    • one year ago
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    i haven't gotten any yet. lets start with #1 @jim_thompson5910

  4. jim_thompson5910
    • one year ago
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    it tells us in #1, that `given that the sum of the numbers is 9` so we know, for a fact, that the two dice add to 9

  5. jim_thompson5910
    • one year ago
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    what are the ways to add to 9 with 2 dice?

  6. Pulsified333
    • one year ago
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    4&5

  7. jim_thompson5910
    • one year ago
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    yep, what else? can you list ALL of the ways to add to 9?

  8. Pulsified333
    • one year ago
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    3&6, 4&5

  9. jim_thompson5910
    • one year ago
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    so put that all together we have 3+6 4+5 5+4 6+3 there are only 4 ways to do this

  10. jim_thompson5910
    • one year ago
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    of these 4 ways, how many have exactly one "6" in them?

  11. jim_thompson5910
    • one year ago
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    you sure?

  12. Pulsified333
    • one year ago
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    2?

  13. jim_thompson5910
    • one year ago
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    yeah 2 3+6 and 6+3

  14. jim_thompson5910
    • one year ago
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    it would be a fraction Probability of exactly one 6, given sum of 9 = (# of sums with 6 in them)/(# of ways to add to 9) = 2/4 = 1/2

  15. jim_thompson5910
    • one year ago
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    ` given that exactly one die shows a 6` so we know die A is 6 or die B is 6 (both cannot be 6 at the same time)

  16. jim_thompson5910
    • one year ago
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    if die A is 6, then what are the possibilities for die B?

  17. Pulsified333
    • one year ago
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    5 and 4?

  18. jim_thompson5910
    • one year ago
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    B could also be 1,2,3 basically it could be anything but 6

  19. jim_thompson5910
    • one year ago
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    if die A is 6, then die B could be 1,2,3,4,5 similarly if die B is 6, then die A could be 1,2,3,4,5

  20. Pulsified333
    • one year ago
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    but doesn't the sum have to be 9?

  21. jim_thompson5910
    • one year ago
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    no, the given here is that one die is 6. That's it

  22. jim_thompson5910
    • one year ago
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    this dice chart may help

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  23. Pulsified333
    • one year ago
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    ok so die B could be 1,2,3,4,5

  24. jim_thompson5910
    • one year ago
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    how many possible outcomes are there if exactly one die is 6?

  25. Pulsified333
    • one year ago
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    but it says What is the probability that the sum of the numbers is 9

  26. jim_thompson5910
    • one year ago
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    we'll get there

  27. jim_thompson5910
    • one year ago
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    in the chart I posted, mark the row that has 6 and the column that has 6. But don't mark the cell that has both 6's. How many cells did you highlight?

  28. Pulsified333
    • one year ago
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    5?

  29. jim_thompson5910
    • one year ago
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    you should count 5 along the '6' row and 5 along the '6' column so 10 in total

  30. jim_thompson5910
    • one year ago
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    how many of those 10, have a sum of 9?

  31. Pulsified333
    • one year ago
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    2?

  32. jim_thompson5910
    • one year ago
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    yes, 6+3 and 3+6 we have 2 sums that have a sum of 9 out of 10 outcomes so 2/10 = 1/5 is the answer to #2

  33. Pulsified333
    • one year ago
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    oh ok, thanks

  34. jim_thompson5910
    • one year ago
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    and for #3, it's almost identical to #2 BUT the key word in #3 is `at least` so it's possible to have both dice be 6

  35. Pulsified333
    • one year ago
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    6&3 3&6

  36. Pulsified333
    • one year ago
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    so is it 1/5? @jim_thompson5910

  37. jim_thompson5910
    • one year ago
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    we have 2 ways to add to 9 (6+3 or 3+6) however, instead of 10 outcomes, we actually have 11. Again, it's possible to have both dice be 6 so it's actually 2/11

  38. Pulsified333
    • one year ago
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    thank you :)

  39. jim_thompson5910
    • one year ago
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    no problem

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