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Math Help - probability help

  1. #1
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    probability help

    A fairground game involves trying to hit a moving target with a gunshot. A round consists of up
    to 3 shots. Ten points are scored if a player hits the target, but the round is over if the player
    misses. Linda has a constant probability of 0.6 of hitting the target and shots are independent of

    one another.


    (a) Find the probability that Linda scores 30 points in a round.

     0.6^3 = 0.216

    The random variable X is the number of points Linda scores in a round.

    (b) Find the probability distribution of X.
    x = 0, 10 , 20 , 30
    p(x) 0.4 0.24 0.144 0.216
    (c) Find the mean and the standard deviation of X.
     E(X) = 11.76

     SD = 11.7

    A game consists of 2 rounds.
    (d) Find the probability that Linda scores more points in round 2 than in round 1.

    I need help woth the last question, 'd', How do I start?


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  2. #2
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    Quote Originally Posted by Tweety View Post


    (a) Find the probability that Linda scores 30 points in a round.

     0.6^3 = 0.216

    The random variable X is the number of points Linda scores in a round.

    (b) Find the probability distribution of X.
    x = 0, 10 , 20 , 30
    p(x) 0.4 0.24 0.144 0.216
    (c) Find the mean and the standard deviation of X.
     E(X) = 11.76

     SD = 11.7

    A game consists of 2 rounds.
    (d) Find the probability that Linda scores more points in round 2 than in round 1.

    I need help woth the last question, 'd', How do I start?


    Hi Tweety,

    For (d), use your results from (b).

    Let's say the result of the first round is X and the result of the second round is Y. There are only 4 possibilities for each, so you should find it easy to list all the pairs (x,y) where x < y. Use independence of X and Y, along with your results from (b), to find the probability of each (x,y) pair. Then add the probabilities up.
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