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Math Help - probability - unsure of what type

  1. #1
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    probability - unsure of what type

    The probability that a certain dart player hits the bullseye with one dart is 0.4.

    a) Find the probability that the player scores at most two bullseyes with 3 darts.
    b) If the probability of scoring at least one bullseye with n darts is greater than 0.9, find the least possible value of n.
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    Quote Originally Posted by shawli View Post
    The probability that a certain dart player hits the bullseye with one dart is 0.4.

    a) Find the probability that the player scores at most two bullseyes with 3 darts.
    b) If the probability of scoring at least one bullseye with n darts is greater than 0.9, find the least possible value of n.
    Have you tried Binomial?

    a) find P(X\leq 2) where X\text{~}Bi(n,p) = X\text{~}Bi(3,0.4)

    b) You will need to work backwards.
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  3. #3
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    It IS binomial, thank you!
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  4. #4
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    I tried to solve b):

    P(X \ge 1) = 1 - P(X = 0)

    0.9 < 1 - P(X = 0)

    0.9  < 1 - 0.6^n

    0.6^n < 0.1

    n  > \frac{ln(0.1)}{ln(0.6)}

    n  > 4.50

    I'm not sure about a), does P(X \le 2) = 1 - P(one\ miss) and then 1 - {3 \choose 1} 0.4^2 0.6 makes sense?
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    Quote Originally Posted by losm1 View Post
    I'm not sure about a), does P(X \le 2) = 1 - P(one\ miss) and then 1 - {3 \choose 1} 0.4^2 0.6 makes sense?
    My understanding is.

    P(X\leq 2) = P(X=0)+P(X=1)+P(X=2)=1-P(X=3)= 1 - {3 \choose 3} \times 0.4^3 \times 0.6^0
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  6. #6
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    That is correct. Thanks
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