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samnatha

help please !! if 20% of the balls produced by the machine are defective find the probability that out of the 4 balls selected at random (i) 2 are defective (ii) not more than 2 are defective i have done part (i) i got 0.1536 but i need help with part (ii)

  • 11 months ago
  • 11 months ago

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  1. amistre64
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    this might be better suited to a binomial setup

    • 11 months ago
  2. samnatha
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    thats what i did for part i and i got that i'm just not sure what to do for the other part

    • 11 months ago
  3. amistre64
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    \[P(2~out~of~4)=\binom{4}{2}~(bad)^2~(good)^2\] \[P(2~out~of~4)=6~(.20)^2~(.80)^2\]

    • 11 months ago
  4. amistre64
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    the second part corresponds to an OR setup P(0) or P(1) or P(2)

    • 11 months ago
  5. samnatha
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    how do you do the second part i have done the first part ..i just need help with the second part

    • 11 months ago
  6. amistre64
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    \[P(0,1,2~out~of~ 4)=6[(.2)^0 (.8)^4+(.2)^1 (.8)^3+(.2)^2 (.8)^2]\]

    • 11 months ago
  7. samnatha
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    where did u get the six from ?

    • 11 months ago
  8. amistre64
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    hmm, i do seem to have been a little amiss with that .... apparently we are not choosing 2 out of 4 each time :/ (4 0) = 1 (4 1) = 4 (4 2) = 6

    • 11 months ago
  9. samnatha
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    ok so i got 0.9728 for my final answer ?

    • 11 months ago
  10. samnatha
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    is that right ?

    • 11 months ago
  11. amistre64
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    that does seem about right. can you see any other errors in my remembering of this?

    • 11 months ago
  12. samnatha
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    nope although i wouldn't have added it up to 6 i would have done each sum seperatly and then added them but thank you for your help :)

    • 11 months ago
  13. amistre64
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    so the liklihood that no more than 2 are defective out of 4 is about 98%, sounds like a winner to me ... good luck :)

    • 11 months ago
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