# 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.

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1. 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.

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2. 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

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3. Can someone answer that, what is the probability that a student is studying French if it is given that he is studying Latin ?

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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

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5. A group consists of 120 students. Of these, 60 are studying French, 50 are studying Spanish and 20 are studying French and Spanish. A student is selected at random. What is the Probability that the student is studying only French?

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