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Test tomm. Need help *Urgent*

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Sorry for posting so many topics, but I really need help on this stuff. I recently lost my work I did on a separate sheet from 2 weeks ago, and now I can't seem to find the answer again.

a fair six-sided die is tossed seven times in a row.

A) What is the probability that a "4" comes up exactly four times? (I got 4375/279936)

B) What is the probability that a "4" comes up an even number of times? (I got 2315/4374)

C) What is the probability that a number higher than "4" Comes up exactly four times (I got 280/2187)

Can anyone help me with this. I need to know how I got these answers again.

  • Math -

    Assistance needed.

  • Test tomm. Need help *Urgent* -

    Tom, I answered part a) in

    for b) using the same argument it would be

    prob(exactly 2 times) + prob(exactly 4 times) + prob(exactly 6 times)

    = C(7,2)(1/6)^2(5/6)^5 + C(7,4)(1/2)^4(5/6)^3 + C(7,6)(1/6)^6(5/6)
    = 70035/279936 which is not what you had

    but check my calculations.

  • Test tomm. Need help *Urgent* -

    B) I believe the middle term in Reiny's formula should be
    = C(7,4)*5^3/6^7
    = 35*125/279,936 = 4375/279,936
    which is the same as the answer to (A)

    C(7,2)(1/6)^2(5/6)^5 = 21*3125/279,936
    = 65625/279,936
    C(7,6)(1/6)^6(5/6) = 7*5/279,936
    = 35/279,936
    Total = 70035/279936 = 0.25018

    I agree with Reiny's final (B) answer, so the (1/2)^4 was probably a typo that should have been (1/6)^4

    C) Since is equally likely to get "5" or "6" four times as it is to get "4" four times, just double the answer to (A). That does not agree with your answer.

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