"Records show that 8% of all college students are foreign students who also smoke. It is also known that 50% of all foreign college students smoke. What percent of the students at this university are foreign?"

I had that:
P(A)=50
P(B)=?
P(A|B)=8

Well, let's have some fun with math, shall we?

If P(A|B) represents the probability of event A happening given that event B has occurred, and we know that P(A) represents the probability of event A occurring, then we can use a little formula called Bayes' Theorem.

Bayes' Theorem states that P(A|B) = (P(B|A) * P(A)) / P(B).

In this case, A represents "foreign college students smoke" and B represents "foreign students at this university."

So, we know that P(A|B) = 8% or 0.08, and P(A) = 50% or 0.5.

To find P(B), we need to figure out P(B|A) or the probability of being a foreign student given that they smoke. Unfortunately, the problem doesn't provide that information.

So, without P(B|A), we can't calculate P(B) specifically. But, we can say that the percentage of students at this university who are foreign is definitely less than or equal to 0.08 or 8%.

In summary, while we can't determine the exact percentage of students who are foreign at this university based on the given information, it's safe to say it could be 8% or lower. And remember, laughter knows no borders, so let's all just clown around together, no matter where we come from!

To find the percent of students at the university who are foreign, you can use the formula for conditional probability:

P(A|B) = P(A ∩ B) / P(B)

In this case, A represents being a foreign college student and B represents smoking.

We know that P(A|B) = 8% (or 0.08) and P(A) = 50% (or 0.5), so we can plug in these values:

0.08 = P(A ∩ B) / 0.5

To find P(A ∩ B), we rearrange the equation:

P(A ∩ B) = 0.08 * 0.5

P(A ∩ B) = 0.04

Now, let's find P(B) using the equation:

P(A ∩ B) = P(B) * P(A|B)

0.04 = P(B) * 0.5

To isolate P(B), divide both sides of the equation by 0.5:

P(B) = 0.04 / 0.5

P(B) = 0.08

Therefore, 8% of the students at this university are foreign.

To find the percentage of students who are foreign, we can use the concept of conditional probability.

Let's break down the information given:

P(A) = 50% - This represents the percentage of all college students who smoke.

P(B) = ? - This represents the percentage of students at this university who are foreign. We need to find this value.

P(A|B) = 8% - This represents the percentage of foreign college students who smoke.

Using the formula for conditional probability, we have:

P(A|B) = P(A ∩ B) / P(B)

Here, P(A ∩ B) represents the probability of both being foreign and smoking, which we do not have directly. But we can calculate it using the information provided.

We know that P(A|B) = 8%, which means that in foreign students, the percentage who smoke is 8%. Since we also know that P(A) = 50%, which represents the percentage of all students who smoke, we can calculate P(B ∩ A) using the formula:

P(B ∩ A) = P(A|B) * P(B)

Here, P(B ∩ A) represents the probability of being both foreign and smoking.

Using the values we have:

P(B ∩ A) = 8% * P(B)

Given that P(A ∩ B) = P(B ∩ A), we can conclude that:

P(A ∩ B) = P(B ∩ A) = 8% * P(B)

Since P(A) = P(A ∩ B) + P(A ∩ B'), where B' represents the complement of B (meaning not foreign), we can substitute the values into the equation:

50% = 8% * P(B) + P(A ∩ B'),

Now, we need to consider that P(B') represents the probability of not being foreign, which can be calculated as 100% - P(B). Therefore:

50% = 8% * P(B) + (100% - P(B))

Simplifying the equation:

50% = 8% * P(B) + 100% - P(B)

Rearranging the equation:

P(B) - 8% * P(B) = 100% - 50%

0.92 * P(B) = 50%

Dividing both sides by 0.92:

P(B) = (50% / 0.92) ≈ 54.35%

Therefore, approximately 54.35% of the students at this university are foreign.

If 8 percent are foreign and smoke, but half of foreign studnens smoke, then why not is 16 precent of the students foreign? http://www.math.cornell.edu/~mec/2008-2009/TianyiZheng/Bayes.html

P(B)=P(A given B)/P(A)=.08/.50=.16