7
8
drink coffee on a regular basis. While some brew their own coffee,
3
4
drink coffee and go to Starbucks to get it. What is the probability that someone goes to Starbucks given they drink coffee?

Question

7
8
 drink coffee on a regular basis. While some brew their own coffee, 
3
4
 drink coffee and go to Starbucks to get it. What is the probability that someone goes to Starbucks given they drink coffee?

BlackTom AI · Accepted Answer

First, I will restate the question and the given data as clearly as possible given the formatting:
- We’re asked: What is the probability that someone goes to Starbucks given they drink coffee?
- There are some numbers interspersed in the text that appear to represent counts: a group that drinks coffee regularly and a subset that goes to Starbucks to get it. The exact counts are garbled in the prompt, but the essential idea is a conditional probability: P(Go to Starbucks | Drinks coffee).

Next, I will break down the concept before tackling any numerical details:
- The conditional probability P(A | B) is defined as P(A ∩ B) / P(B), which, in a count form, is (number of people who both go to Starbucks and drink coffee) divided by (the total number of people who drink coffee).
- If we had a clean tally of the two groups:
  - Total coffee drinkers: N(coffee)
  - Coffee drinkers who go to Starbucks: N(Starbucks ∩ coffee)
  Then the probability would be N(Starbucks ∩ coffee) / N(coffee).

Now, addressing the provided (garbled) numbers and the answer field:
- The prompt contains fragments like '7', '8', '3', '4', which seem to be intended as counts, but they are not clearly linked to the categories. Because the counts aren’t clearly labeled, we cannot independently verify the ratio from the text alone.
- The answer field lists '6/7 = 0.86' as a proposed result. If we interpret this as the intended ratio, it implies that among the coffee drinkers, 6 out of 7 go to Starbucks (i.e., N(Starbucks ∩ coffee) = 6 and N(coffee) = 7).

With the above interpretation, here is how the reasoning would support 6/7:
- Suppose the total number of people who drink coffee is 7.
- Suppose the number of those coffee drinkers who go to Starbucks is 6.
- Then the conditional probability P(Starbucks | drinks coffee) = 6 / 7, which equals approximately 0.86.

Now, considering why other interpretations or misreadings would be incorrect:
- If you misinterpret the counts (for example, if there were 7 coffee drinkers and 8 Starbucks-goers, or if the Starbucks-goers were counted separately from the total coffee drinkers), you could arrive at a different ratio or even a value greater than 1 if misapplied. The key is to ensure that the denominator is the total number of coffee drinkers, and the numerator is those among them who go to Starbucks.
- If the data were incomplete or misaligned, attempting to form a ratio would lead to an incorrect probability, because you must condition on the event 'drinks coffee' and count only from that subset.

In summary, assuming the intended counts are: total coffee drinkers = 7 and among them those who go to Starbucks = 6, the conditional probability would be 6/7 (about 0.86). The core point is applying the conditional-probability principle correctly and ensuring the numerator and denominator refer to the same conditioning set (coffee drinkers).

If you have access to the clean, labeled counts (total coffee drinkers and among them those who go to Starbucks), you can plug them into the formula P(Starbucks | drinks coffee) = N(Starbucks ∩ coffee) / N(coffee) to obtain the exact probability.

MAT-SEC2 B Probability Quiz (Conditional Probability)

7 8 drink coffee on a regular basis. While some brew their own coffee, 3 4 drink coffee and go to Starbucks to get it. What is the probability that someone goes to Starbucks given they drink coffee?

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