There are 30 students in the class. 16 of them study french and 21 study spanish. They all study at least one of the two languages. What is the probability that a student chosen at random studies french only?
If x study both, then
16+21-x = 30
x = 7
so, 16-7 = 9 study French only
now finish it off
To find the probability that a student chosen at random studies French only, we need to find out how many students study French only and then divide it by the total number of students.
We know that there are 30 students in total, and 16 of them study French. However, we don't know how many of these 16 students also study Spanish. To find out how many students study French only, we can subtract the number of students who study both French and Spanish from the total number of students who study French.
To find the number of students who study both French and Spanish, we subtract the number of students who study Spanish from the total number of students.
Number of students who study both French and Spanish = Total number of students studying French and Spanish - Number of students studying Spanish
Number of students who study both French and Spanish = 16 - 21 = -5
Since we can't have a negative number of students, it means there must be an error in the given information. It's not possible for 16 students to study French and 21 students to study Spanish, while there are only 30 students in total. Please double-check the given information and provide the correct numbers.
To find the probability that a student chosen at random studies French only, we need to determine the number of students who study French only and divide it by the total number of students.
Let's break it down step by step:
1. We know that there are 30 students in total.
2. Out of these 30 students, 16 of them study French and 21 study Spanish. However, we need to subtract the students who study both languages, as we are looking for those who study French only.
3. To calculate the number of students who study French only, we can subtract the students who study both languages from the total number of students who study French.
Let's denote "F" as the number of students who study French only, "B" as the number of students who study both languages, and "S" as the number of students who study Spanish only. We have the following equations:
F + B = 16 (The total number of students who study French)
B = 21 - S (The number of students who study both languages)
4. Let's solve these equations simultaneously. From equation 2, we can substitute the value of B in equation 1:
F + (21 - S) = 16
F + 21 - S = 16
F - S = 16 - 21
F - S = -5
5. Since we have two unknowns (F and S) and only one equation, we need an additional piece of information to solve the problem. Without this information, we can't determine the exact number of students who study French only.
However, we can find the range of possible values for the probability. Since the total number of students is 30, the maximum number of students who study French only is 16 (when no students study both languages), and the minimum number is 0 (when all students study both languages). Therefore, the probability of a student chosen at random studying French only lies between 0 and 16/30.
In conclusion, without further information, we cannot determine the exact probability that a student chosen at random studies French only. However, we can state that the probability lies between 0 and 16/30.