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Math Help - Probability

  1. #1
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    Probability

    Need some help with these please:

    The probability that I catch a fish when it is raining is 0.65. The probability that I catch a fish when it is not raining is 0.40. The probability that it will rain tomorrow is 0.70. What is the probability that I catch a fish if I go fishing tomorrow?

    In a contest, I get to draw a number from 1-10 from a hat, and roll a die. I win if I get either an odd number from the hat, OR a 3 on the die. What is the probability that I will win with 1 draw and 1 roll?

    and

    P(E)=0.3, P(F)=0.5, P(E∩F)=0.1
    And I have to find:
    P(E|F) and P(F|E)

    Thanks for any help.
    Last edited by StackFryer; November 30th 2006 at 03:00 PM.
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  2. #2
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    For #1. The probability of a catch, C, depends on rain, R, and no rain, Rí.
    \begin{array}{rcl}<br />
 P(C) & = & P(CR) + P(CR') \\ <br />
  & = & P(C|R)P(R) + P(C|R')P(R') \\ <br />
 \end{array}.

    For #2. You have independence so:
    \begin{array}{rcl}<br />
 P(O \cup 3) & = & P(O) + P(3) - P(O \cap 3) \\ <br />
  & = & P(O) + P(3) - P(O)P(3) \\ <br />
 \end{array}.

    For #3.
    P(A|B) = \frac{{P(A \cap B)}}{{P(B)}}
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  3. #3
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    Quote Originally Posted by Plato View Post
    For #1. The probability of a catch, C, depends on rain, R, and no rain, Rí.
    \begin{array}{rcl}<br />
 P(C) & = & P(CR) + P(CR') \\ <br />
  & = & P(C|R)P(R) + P(C|R')P(R') \\ <br />
 \end{array}.

    For #2. You have independence so:
    \begin{array}{rcl}<br />
 P(O \cup 3) & = & P(O) + P(3) - P(O \cap 3) \\ <br />
  & = & P(O) + P(3) - P(O)P(3) \\ <br />
 \end{array}.

    For #3.
    P(A|B) = \frac{{P(A \cap B)}}{{P(B)}}
    So for #2, I got 0.577.

    #3 I got (P|E)=0.2 and (P|F)=0.333...

    are those right? I'm still working on #1.
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