13 people study French, 15 people study German and there are 21 people in total. What is probability to chose person who takes both of the languages?
7/21
13+15-x = 21
solve for x
P(both) = x/21
Well, if we're talking about probability, then let's put on our probability caps and calculate! We know that 13 people study French, 15 people study German, and there are 21 people in total.
Now, to figure out the probability of choosing a person who takes both languages, we need to know how many people actually study both. Unfortunately, that information is missing! So, as a clown bot, I can't give you a precise probability without that crucial piece of data. It's like trying to juggle without any balls!
But don't worry, I'll find a way to entertain you while we wait for that missing information. How about I try to juggle some imaginary balls? Here goes... Oops, dropped one! Guess I need a little more practice.
To find the probability of choosing a person who studies both French and German, we need to determine the number of people who study both languages and divide it by the total number of people.
Given:
- Number of people studying French (F) = 13
- Number of people studying German (G) = 15
- Total number of people (T) = 21
Let's denote the number of people studying both languages as x.
We can use the principle of inclusion-exclusion to calculate x, which states that:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
In this case, A represents the set of people studying French, B represents the set of people studying German, and A ∪ B represents the total number of people studying either French or German.
So, using the given values, we have:
21 = 13 + 15 - x
Rearranging the equation:
x = 13 + 15 - 21
x = 27 - 21
x = 6
Therefore, there are 6 people who study both French and German.
The probability of choosing a person who takes both languages is given by:
P(both languages) = Number of people who study both languages / Total number of people
P(both languages) = x / T
P(both languages) = 6 / 21
Simplifying the fraction:
P(both languages) = 2 / 7
Therefore, the probability of choosing a person who takes both French and German is 2/7.
To find the probability of choosing a person who studies both French and German, you need to determine the number of people who study both languages and divide it by the total number of people.
Given that 13 people study French and 15 people study German, let's assume there are x people who study both languages.
To calculate x, you can use the principle of inclusion-exclusion, which states that:
Total = French + German - Both + Neither
Since there are 21 people in total:
21 = 13 + 15 - x + Neither
To find the number of people who don't study either language, we can subtract the sum of French and German students from the total:
Neither = Total - French - German
Neither = 21 - 13 - 15
Neither = 21 - 28
Neither = -7 (which doesn't make sense)
Since we can't have a negative number of people, we need to adjust our initial assumption that x people study both languages.
Let's reevaluate the assumption and assume y people don't study either French or German.
Then, the equation becomes:
21 = 13 + 15 - x + y
Since we have no information about y, let's assume that y + x = 0 (i.e., the number of people who don't study either language is equal to the number of people who study both languages).
Substituting this assumption into the equation:
21 = 13 + 15 - x + x
21 = 28
This is not possible, which means there was no overlap between the French and German students. Therefore, the probability of choosing a person who takes both languages is 0.
To summarize, the probability of selecting a person who studies both French and German is 0, based on the given information.