Results 1 to 2 of 2

Math Help - A basketball player attempts a free throw...

  1. #1
    Member
    Joined
    Sep 2006
    Posts
    75

    A basketball player attempts a free throw...

    A basketball player attempts a free throw. If he is successful, he can attempt a second free throw. If P is his probability of a successful free throw, and if his probability of making 0 points is equal to that of making 2 points, what is P? (Round the answer to the nearest thousandth.)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    Quote Originally Posted by ceasar_19134 View Post
    A basketball player attempts a free throw. If he is successful, he can attempt a second free throw. If P is his probability of a successful free throw, and if his probability of making 0 points is equal to that of making 2 points, what is P? (Round the answer to the nearest thousandth.)
    Let's say that: P=\frac{1}{x}

    So the odds of making a shot are: \frac{1}{x}

    The odds of making two shots are: \frac{1}{x}\times \frac{1}{x}=\frac{1}{x^2}

    The odds of missing the first shot are: 1-\frac{1}{x}=\frac{x-1}{x}

    Which means that: \frac{x-1}{x}=\frac{1}{x^2}

    Multiply both sides by x to get: x-1=\frac{1}{x}

    Mutiply again: x^2-x=1

    Subtract 1 from both sides: x^2-x-1=0

    Use the quadratic equation: x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

    Substitute: x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-1)}}{2(1)}

    Solve: x=\frac{1\pm\sqrt{5}}{2}

    That gives that: x=1.61803399, -0.618033989

    Since it can't be negative, we know that: x=1.61803399

    Remember: P=\frac{1}{x}

    Substitute: P=\frac{1}{1.61803399}

    Solve: P=0.618033988

    Round to get: \boxed{P\approx 0.618}

    BUT CHECK MY ARITHMETIC
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: September 23rd 2011, 11:57 PM
  2. X Attempts at a certain die roll with a retry
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 5th 2011, 11:03 AM
  3. probability: free throw shooter
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: April 11th 2009, 04:54 PM
  4. basketball player
    Posted in the Statistics Forum
    Replies: 2
    Last Post: August 10th 2006, 08:07 PM
  5. Basketball player, ballistics
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: June 27th 2006, 12:50 PM

Search Tags


/mathhelpforum @mathhelpforum