# Thread: need help with this probability question

1. ## need help with this probability question

Hey all,

I've tried amny times trying to solve this question but unsuccessful. I'll appreciate it if anyone can help me with this.

The probability that it is windy wen it rains is 0.5, and the probability that it is raining when it is windy is 0.3, and the probability that it is raining or windy is 0.7.

a)find the probability that it is raining.
b)find the probability that it is windy.
c)find the probability that it is raining and windy.

i know that
P(W|R) = 0.5
P(R|W)=0.3
P(RuW)=0.7

Thanks

2. Originally Posted by shellshock
Hey all,

I've tried amny times trying to solve this question but unsuccessful. I'll appreciate it if anyone can help me with this.

The probability that it is windy wen it rains is 0.5, and the probability that it is raining when it is windy is 0.3, and the probability that it is raining or windy is 0.7.

a)find the probability that it is raining.
b)find the probability that it is windy.
c)find the probability that it is raining and windy.

i know that
P(W|R) = 0.5
P(R|W)=0.3
P(RuW)=0.7

Thanks
Draw a Karnaugh table to help visualise things:

$\displaystyle \begin{tabular}{l | c | c | c} & R & R' & \\ \hline W & a & b & a + b \\ \hline W' & c & d & c + d\\ \hline & a + c & b + d & 1 \\ \end{tabular}$

Then it should be clear that:

$\displaystyle \Pr(W | R) = \frac{a}{a + c} = \frac{1}{2} \Rightarrow c - a = 0$ .... (1)

$\displaystyle \Pr(R | W) = \frac{a}{a + b} = \frac{3}{10} \Rightarrow 3b - 7a = 0$ .... (2)

$\displaystyle \Pr(R \cup W) = a + b + c = \frac{7}{10}$ .... (3)

$\displaystyle a + b + c + d = 1$ .... (4)

Solve equations (1), (2), (3) and (4) simultaneously for a, b, c and d and then answer the given questions using the Karnaugh table.

3. Thanks, that helped a lot.