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.

 

[blue_raver22]

Hello there,

Thank you for reaching out with your probability question. It's great to see that you are preparing for the GRE and practicing these types of questions.

To answer your first question, if Ralph uses an umbrella, the probability that Laura did not use an umbrella can be found by using the complement rule. This means that the probability of an event not happening is equal to 1 minus the probability of the event happening. In this case, the probability of Ralph using an umbrella is 0.25, which means that the probability of Laura not using an umbrella is 1-0.25=0.75.

For your second question, the probability that Ralph will use an umbrella can be calculated by using the law of total probability. This states that the probability of an event happening is equal to the sum of the probabilities of all the possible outcomes. In this case, we have two possible outcomes: either Laura uses an umbrella or she doesn't. So the probability of Ralph using an umbrella is equal to the probability of Laura using an umbrella (0.70) multiplied by the probability of Ralph using an umbrella if Laura uses one (0.25), plus the probability of Laura not using an umbrella (0.30) multiplied by the probability of Ralph using an umbrella if she doesn't (0.50). This gives us a total probability of 0.70*0.25 + 0.30*0.50 = 0.175 + 0.15 = 0.325.

I hope this helps you with your question. Probability questions can be tricky, but with practice and understanding of the rules, you will be able to solve them with ease. All the best for your GRE preparation!