Of 120 students, 60 are studying French, 50 are studying Latin and 20 are studying French and Latin. Find the probability that a student is: (a) studying French or Latin and (b) studying neither.
P(F or L) =P(F) + P(L) - P(F and L)
= 60/120 + 50/120 - 20/120
= 90/120
= 3/4
or you could make Venn diagrams showing overlapping circles for French and Latin within a universal set of 120
enter 20 in the intersection of the two circles.
then 40 would go in the non-overlapping part of French and 30 in the non-overlapping part of Latin
total of inside of both circles = 40+20+30 = 90
So Prob of F or L is 90/120 = 3/4
for b) number of students outside the two circles is 120-90 = 30
so Prob of neither F or L is 30/120 = 1/4
Of 120 students, 60 are studying French, 50 are studying Spanish, and 20 are studying French and Spanish. If a student is chosen at random, find the probability that the student (i) is studying French or Spanish, (ii) is studying neither French nor Spanish
Assuming that the 60 and 50 are studying only one language, there cannot be 20 studying both out of 120 students. Do you have your total number of students wrong?
Repost with correct data. Thanks for asking.
Can someone answer that, what is the probability that a student is studying French if it is given that he is studying Latin ?
(a) Ah, let's join the language party! To find the probability that a student is studying French or Latin, we need to add the number of students studying French and the number of students studying Latin, and then subtract the number of students studying both languages. So, we have 60 + 50 - 20 = 90.
Out of 120 students in total, 90 are studying French or Latin.
Therefore, the probability that a student is studying French or Latin is 90/120, which simplifies to 3/4 or 75%.
(b) Now, let's turn things around and find the probability that a student is studying neither French nor Latin. To do this, we subtract the number of students studying French or Latin from the total number of students.
So, we have 120 - 90 = 30.
Out of 120 students, 30 are studying neither French nor Latin.
Therefore, the probability that a student is studying neither French nor Latin is 30/120, which simplifies to 1/4 or 25%.
Oh, those students always going against the language flow!
To find the probability that a student is studying French or Latin, we need to calculate the number of students studying French, the number of students studying Latin, and the number of students studying both French and Latin.
(a) Probability of studying French or Latin:
The number of students studying French or Latin can be calculated by adding the number of students studying French and the number of students studying Latin, and subtracting the number of students studying both French and Latin to avoid double counting:
Number of students studying French or Latin = Number of students studying French + Number of students studying Latin - Number of students studying both French and Latin
Number of students studying French = 60
Number of students studying Latin = 50
Number of students studying both French and Latin = 20
Number of students studying French or Latin = 60 + 50 - 20 = 90
The probability of a student studying French or Latin can now be calculated by dividing the number of students studying French or Latin by the total number of students:
Probability of studying French or Latin = Number of students studying French or Latin / Total number of students
Total number of students = 120
Probability of studying French or Latin = 90 / 120 = 3/4 or 0.75
Therefore, the probability that a student is studying French or Latin is 3/4 or 0.75.
(b) Probability of studying neither:
To find the probability that a student is studying neither French nor Latin, we need to subtract the probability of studying French or Latin from 1, since the probabilities of all possible outcomes should add up to 1.
Probability of studying neither = 1 - Probability of studying French or Latin
Probability of studying neither = 1 - 0.75 = 0.25
Therefore, the probability that a student is studying neither French nor Latin is 0.25 or 1/4.