Results 1 to 3 of 3

Math Help - last question

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    139

    last question

    This should be the last.

    A college basketball player who sinks 75% of his free throws comes to the line to shoot a "one and one" (if the first shot id successful he is allowed a second shot, but no second shot is taken if the first is missed; one point is scored for each successfull shot). Assume that the outcome of the second shot, if any, is independent of that of the first. Find the expected number of points resulting from the "one and one". Compare this with the expected number of points from a "two-shot foul", where a second shot is allowed, irrespective of the outcome of the first.

    I do not know. I do not know.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,706
    Thanks
    625
    Hello, 0123!

    A college basketball player who sinks 75% of his free throws
    comes to the line to shoot a "one and one".
    (If the first shot is successful he is allowed a second shot,
    but no second shot is taken if the first is missed.
    One point is scored for each successfull shot).

    Assume that the outcome of the second shot, if any, is independent of that of the first.

    Find the expected number of points resulting from the "one and one".

    There are three possible outcomes:

    [1] He misses the first shot: 0 points
    [2] He makes the first shot and misses the second: 1 point
    [3] He makes both shots: 2 points

    \begin{array}{cccccc}<br />
\text{Points} & & & \text{Probability} \\ \hline<br />
0 & P(\sim\!1^{st}) & = & & & 0.25\\<br /> <br />
1 & P(1^{st} \wedge \sim\!2^{nd}) & = & (0.75)(0.25) & = & 0.1875\\<br /> <br />
2 & P(1^{st} \wedge 2^{nd}) & = & (0.75)(0.75) & = & 0.5625<br />
\end{array}


    E \;=\;(0)(0.25) + (1)(0.1875) + (2)(0.5625) \;=\;{\color{blue}\boxed{1.3125}}



    Compare this with the expected number of points from a "two-shot foul",
    where a second shot is allowed, irrespective of the outcome of the first.

    There are four possible outcomes:

    [1] He misses both shots: 0 points
    [2] He make the first, misses the second: 1 point
    [3] He misses the first, makes the second: 1 point
    [4] He makes both shots: 2 points

    \begin{array}{cccccc}<br />
\text{Points} & & & \text{Probability} \\ \hline<br />
0 & P(\sim\!1^{st} \wedge \sim\!2^{nd}) & = & (0.25)(0.25) & = & 0.0625\\<br /> <br />
1 & P(1^{st} \wedge \sim\!2^{nd}) & = & (0.75)(0.25) & = & 0.1875\\<br /> <br />
1 & P(\sim\!1^{st} \wedge 2^{nd}) & = & (0.25)(0.75) & = & 0.1875 \\<br /> <br />
2 & P(1^{st} \wedge 2^{nd}) & = & (0.75)(0.75) & = & 0.5625<br />
\end{array}


    E \;=\; (0)(0.0625) + (1)(0.1875) + (1)(0.1875) + (2)(0.5625) \;=\;{\color{blue}\boxed{1.5}}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2006
    Posts
    139
    Thank you so much Soroban it appears to clear and clean now you've made it.
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum