What Is the Probability Ralph Uses an Umbrella If Laura Does Not?

[confusedonpro]

Homework Statement

Hello everyone

New here and doing some random probability questions in prep for the GRE. I found one and I know it is simple, but I am stumped, and there is no answer online. Here it is--any help is much appreciated.

Ralph is considering whether to use an umbrella. Previously, Ralph's friend Laura had used an umbrella 70% of the time. If Laura does not use an umbrella, the probability that Ralph will use an umbrella is .50. If Laura does use an umbrella, the probability that Ralph uses an umbrella is .25.

a) If Ralph uses an umbrella, what is the probability that Laura did not use an umbrella?
b)What is the probability that Ralph will use an umbrella?

Thanks so much in advance.

Homework Equations

The Attempt at a Solution

 

[nobahar]

Hello!
Apologies if this is not correct, but I think the following may help!
You know the P(Ralph uses the umbrella l Laura uses the umbrella), which is 0.25, and you know the P(Ralph using the umbrella l Laura does not use the umbrella), which is 0.5. You also know the denominator in the calculations for these conditional probabilities, which are 0.7 and 0.3, respectively. Using this information should give you the p(Ralph and Laura using an umbrella) and P(Ralph using an umbrella and Laura not using an umbrella). I think this gives enough information to work out the values to calculate P(Laura not using an umbrella l Ralph uses an umbrella).
I really hope that is of some help.

 

[vela]

Look into conditional probability and Bayes' theorem.

http://en.wikipedia.org/wiki/Conditional_probability
http://en.wikipedia.org/wiki/Bayes'_theorem