Question

There are two coffee shops nearby, Coffee Shop A and Coffee Shop B. Based on your coffee habits, the probability of you going to Coffee Shop A is 0.2. Moreover, Coffee Shop A has better croissants than Coffee Shop B. Given that you go to Coffee Shop A, the probability of ordering a croissant is 0.6 and if you go to Coffee Shop B, the probability of ordering a croissant is 0.1. Use this information to calculate the following probabilities. Write your answers as decimal numbers rounded to two decimal places. a. The probability of going to Coffee Shop A and ordering a croissant. [Hint: Let A represent the event that you go to Coffee Shop A, and C represent the event that you order a croissant. You're being asked to calculate $P(A \text{ and } C)$.] b. The probability of ordering a croissant. [Hint: You're being asked to calculate $P(C)$.] c. The probability of going to Coffee Shop A given that you order a croissant. [Hint: You're being asked to calculate $P(A \mid C)$.] d. Given that you order a croissant, is it more likely that you go to Coffee Shop A than Coffee Shop B?

          There are two coffee shops nearby, Coffee Shop A and Coffee Shop B. Based on your coffee habits, the probability of you going to Coffee Shop A is 0.2. Moreover, Coffee Shop A has better croissants than Coffee Shop B. Given that you go to Coffee Shop A, the probability of ordering a croissant is 0.6 and if you go to Coffee Shop B, the probability of ordering a croissant is 0.1. Use this information to calculate the following probabilities. Write your answers as decimal numbers rounded to two decimal places.

a. The probability of going to Coffee Shop A and ordering a croissant. [Hint: Let A represent the event that you go to Coffee Shop A, and C represent the event that you order a croissant. You're being asked to calculate $P(A \text{ and } C)$.]

b. The probability of ordering a croissant. [Hint: You're being asked to calculate $P(C)$.]

c. The probability of going to Coffee Shop A given that you order a croissant. [Hint: You're being asked to calculate $P(A \mid C)$.]

d. Given that you order a croissant, is it more likely that you go to Coffee Shop A than Coffee Shop B?

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there are two coffee shops nearby coffee shop a and coffee shop b based on your coffee habits the probability of you going to coffee shop a is 02 moreover coffee shop a has better croissants 55062

Added by Christina B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jason Horton

04/11/2022

Step 1

- B: Event that you go to Coffee Shop B. - C: Event that you order a croissant. Given probabilities: - $P(A) = 0.2$ - Since there are only two coffee shops, $P(B) = 1 - P(A) = 1 - 0.2 = 0.8$. - $P(C \mid A) = 0.6$ (Probability of ordering a croissant given you go Show more…

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There are two coffee shops nearby, Coffee Shop A and Coffee Shop B. Based on your coffee habits, the probability of you going to Coffee Shop A is 0.2. Moreover, Coffee Shop A has better croissants than Coffee Shop B. Given that you go to Coffee Shop A, the probability of ordering a croissant is 0.6 and if you go to Coffee Shop B, the probability of ordering a croissant is 0.1. Use this information to calculate the following probabilities. Write your answers as decimal numbers rounded to two decimal places. a. The probability of going to Coffee Shop A and ordering a croissant. [Hint: Let A represent the event that you go to Coffee Shop A, and C represent the event that you order a croissant. You're being asked to calculate $P(A \text{ and } C)$.] b. The probability of ordering a croissant. [Hint: You're being asked to calculate $P(C)$.] c. The probability of going to Coffee Shop A given that you order a croissant. [Hint: You're being asked to calculate $P(A \mid C)$.] d. Given that you order a croissant, is it more likely that you go to Coffee Shop A than Coffee Shop B?

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0:00 All right.

00:01 In your question, you're given probabilities for ordering a beverage or a drink, probability for ordering food, probability of ordering beverage or food.

00:12 Okay, so this is a perfect situation for a bend diagram because there's going to be some overlap here.

00:19 Some people ordered a drink, also ordered food, and so on.

00:23 So i'm going to start with probability of a or b.

00:27 And basically what i know is that the three regions of these two circles, we have the overlap region and the non -overlap regions, would have to add up to that .98 total.

00:40 But i can't just put .645 in for a and 0 .45 in for b because that totals over 100%, which is not possible.

00:50 So i'm going to use the formula for a probability of a or b, and it looks like, usually this is like a u -shaped symbol.

01:02 And the way we find that is the probability of a plus the probability of b minus the probability of a and.

01:15 Okay, so we know this.

01:17 That was given to us as 0 .98, and we know probability of a is 0 .65, probability of b is 0 .45, and we don't know this value, probability of a and b.

01:34 Okay, so what i end up with here is these two values would add up to 1 .1.

01:45 So let me work this over here a little bit.

01:54 All right, so i would subtract 1 .1, just on a little algebra here, and we end up with a negative .12 equals negative probability of a and b...

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