# Math Help - Probability

1. ## 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.

2. For #1. The probability of a catch, C, depends on rain, R, and no rain, R’.
$\begin{array}{rcl}
P(C) & = & P(CR) + P(CR') \\
& = & P(C|R)P(R) + P(C|R')P(R') \\
\end{array}.$

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

For #3.
$P(A|B) = \frac{{P(A \cap B)}}{{P(B)}}$

3. Originally Posted by Plato
For #1. The probability of a catch, C, depends on rain, R, and no rain, R’.
$\begin{array}{rcl}
P(C) & = & P(CR) + P(CR') \\
& = & P(C|R)P(R) + P(C|R')P(R') \\
\end{array}.$

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

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.