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Syamantak

Probability of Rain on a Day=0.2 What is the probability of raining atleast 2 days in a week ?

  • 11 months ago
  • 11 months ago

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  1. amistre64
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    there are 2 ways to approach this

    • 11 months ago
  2. amistre64
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    out of 7 days in a week, it would be easier to calculate the compliment statement of: P(rain at most 1 day out of 7)

    • 11 months ago
  3. amistre64
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    P(0) + P(1)

    • 11 months ago
  4. amistre64
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    ... or is the compliment; does not rain at most 1 day out of the week?

    • 11 months ago
  5. amistre64
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    P(0) + P(1) at most 1 day of rain P(2) + P(3) + P(4) + P(5) + P(6) + P(7) at least 2 days of rain in any case .... the long way is: \[\sum_{2}^{7}~\binom{7}{r}~.2^r~.8^{7-r}\]

    • 11 months ago
  6. Syamantak
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    @amistre64 how do we solve the equation ?

    • 11 months ago
  7. amistre64
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    im thinking the 1 - P0+P1 is quicker "by hand"\[1-\binom{7}{0}~.2^0.8^7-\binom{7}{1}~.2^1.8^6\]

    • 11 months ago
  8. Syamantak
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    Actually I don't know summation and other things could you give it to me in a simple version @amistre64

    • 11 months ago
  9. amistre64
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    the (7 0) is just another way to write 7 "choose" 0, by this time you should have already gone thru the permuatation and combination material 7 C 0 is a common notation, but some texts use C(7,0) does any of that look familiar?

    • 11 months ago
  10. Syamantak
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    No,nothing looks familiar to me.Could you write the equation in a multiplication/addition/division/subtraction format @amistre64

    • 11 months ago
  11. amistre64
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    I already did. But if you do not know how to determine the number of ways to choose 0 from a set of 7, or the number of ways to choose 1 from a set of 7; then you really need to go back and review that material. The rest of the setup is elementary ....

    • 11 months ago
  12. Syamantak
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    Can you solve the equation step by step @amistre64

    • 11 months ago
  13. amistre64
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    not without having to try to teach you a chapters worth of material first. consider this tho: if you have 7 things in front of you, what is the number of ways you can simply walk away and choose none of them?

    • 11 months ago
  14. Syamantak
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    \[\infty \] ways

    • 11 months ago
  15. amistre64
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    :) there is really only 1 way to choose none of them, the choice to walk away is only 1 option. 7 "choose" 0 is equal to 1; in fact anything "choose" 0 = 1

    • 11 months ago
  16. amistre64
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    how, consider these 7 things, but you can only choose one of them; how many ways is there to choose 1 of them?

    • 11 months ago
  17. Syamantak
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    7 ways

    • 11 months ago
  18. amistre64
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    lets have 7 things to choose from: a b c d e f g we can choose a or we can choose b or we can choose c or we can choose d or we can choose e or we can choose f or we can choose g 7 "choose" 1 is equal to ..7 do you agree?

    • 11 months ago
  19. amistre64
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    oh, you do agree :) good.

    • 11 months ago
  20. amistre64
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    now we can do the elementary stuff \[ 1 - (1~.2^0~.8^7+7~.2^1~.8^6)\]

    • 11 months ago
  21. Syamantak
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    Ok so what will it be ?

    • 11 months ago
  22. amistre64
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    most likely it will be whatever the calculator generates as an answer for you after you punch in the correct keys :/

    • 11 months ago
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