How Do Conditional Probabilities Affect Ralph's Decision to Use an Umbrella?

[confusedonpro]

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.

 

[dacruick]

So this first thing I notice is that whether or not ralph uses an umbrella, laura uses one70% of the time. So when they say if ralph uses an umbrella what is the probability that laura doesn't, that's the same question as, what is the probability that laura does not use an umbrella.

Then the next question is what ist he probability that ralph will use an umbrella. So what you want to do here is split it up into cases.

Case 1: 70% of the time laura uses one, and out of the 70% of times that laura uses one, ralph uses one 50% of the time.

Case 2: 30% of the time laura does not use one, out of that 30%, ralph uses an umbrella 25% of the time. if you have any questions feel free to ask .

 

[confusedonpro]

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.

Looks like I posted in the wrong forum. Woops. Sorry. Please delete.

 

[confusedonpro]

So this first thing I notice is that whether or not ralph uses an umbrella, laura uses one70% of the time. So when they say if ralph uses an umbrella what is the probability that laura doesn't, that's the same question as, what is the probability that laura does not use an umbrella.

Then the next question is what ist he probability that ralph will use an umbrella. So what you want to do here is split it up into cases.

Case 1: 70% of the time laura uses one, and out of the 70% of times that laura uses one, ralph uses one 50% of the time.

Case 2: 30% of the time laura does not use one, out of that 30%, ralph uses an umbrella 25% of the time. if you have any questions feel free to ask .

Thanks for that info. I guess I am still confused regarding the actual answers to A and B. For A, I get 15% (.5 * .3). For B, I get .35. However, I just KNOW I am wrong.