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Ocr Review Probability question 7 From year 2.

Really need some help with this question I don't know where to start.

Q) In a year cohort the probability that a
randomly chosen student is studying French is 0.84, the probability that a randomly chosen student is studying German is 0.65, and 8% of the cohort study neither French nor German. Find the probability that a randomly chosen student is studying both French and German.
Reply 1
Avatar for Rabbit2
Rabbit2
18
Original post by Omarblack
Really need some help with this question I don't know where to start.

Q) In a year cohort the probability that a
randomly chosen student is studying French is 0.84, the probability that a randomly chosen student is studying German is 0.65, and 8% of the cohort study neither French nor German. Find the probability that a randomly chosen student is studying both French and German.

Ok, i would assume that the two 'events' - i.e. studying French or studying German were "disjoint" - that is, the occurrence of one does not affect the likelihood of the other. Given that, the probability of studying both French AND German should be the product of the probabilities - i.e. .5460 . Hope that helps.. Cheers.
Reply 2
Avatar for Omarblack
Omarblack
OP
9
Wait so the product is both of the probabilities of the event occurring multiplied by each other? And was that percentage important to tackle this question?
Reply 3
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mqb2766
21
Original post by Omarblack
Wait so the product is both of the probabilities of the event occurring multiplied by each other? And was that percentage important to tackle this question?

Drawing a Venn diagram and posting in the maths forum, rather than languages, would help. But what rule do you know relating
p(AuB)
and
p(AnB)
(edited 3 years ago)
Reply 4
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Omarblack
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9
Original post by mqb2766
Drawing a Venn diagram and posting in the maths forum, rather than languages, would help. But what rule do you know relating
p(AuB)
and
p(AnB)

I Don't know how to draw a venn diagram for this, im so confused. the formulas i know are P(a U b) = P(a) + P(b) - P(A n B).

the textbook tells me that the answer is 0.57 but the other guy got 0.546?
Reply 5
Avatar for mqb2766
mqb2766
21
Original post by Omarblack
I Don't know how to draw a venn diagram for this, im so confused. the formulas i know are P(a U b) = P(a) + P(b) - P(A n B).

the textbook tells me that the answer is 0.57 but the other guy got 0.546?

So what do you get when you use that formula? Rearrange in terms of
p(AnB) = ...

A and B are not independent, so you don't simply multiply p(A) and p(B) together to get p(AnB). Also Venn diagrams are on the gcse syllabus, so it may be worth reviewing. They're not absolutely necessary for this problem, but helpful if you're stuck.
(edited 3 years ago)
Reply 6
Avatar for Omarblack
Omarblack
OP
9
P(F) + P(G) = 1.49.

but how do i work out the P(A U B)? I don't know how to get to that answer? Do I use the percentage?

How do i know if an event is independent of each other?

ok i guess i also got to revise venn diagrams again, probability is my weakest.
Reply 7
Avatar for mqb2766
mqb2766
21
Original post by Omarblack
P(F) + P(G) = 1.49.

but how do i work out the P(A U B)? I don't know how to get to that answer? Do I use the percentage?

How do i know if an event is independent of each other?

ok i guess i also got to revise venn diagrams again, probability is my weakest.

F & G are not independent. There is nothing in the question which states it, and it was wrong to assume that they were independent. In general, if
p(AnB) = p(A)p(B)
then they are independent. Its worth reviewing what independence means (venn diagrams help again), rather than just learning a formula.

You know how many people don't take either F or G (8% or 0.08), so
p(FuG) = 1 - 0.08
Then you just plug it in to get the joint probability p(FnG). A venn diagram does make it clear and is worth revising.
(edited 3 years ago)
Reply 8
Avatar for Omarblack
Omarblack
OP
9
Ah I calculated it now using. A venn diagram. Took me quite some time. But I got 0.57 as the p.
Reply 9
Avatar for mqb2766
mqb2766
21
Original post by Omarblack
Ah I calculated it now using. A venn diagram. Took me quite some time. But I got 0.57 as the p.

Good. Its worth noting that a venn diagram and that formula go hand in hand. The venn is used to visualize the data.
Reply 10
Avatar for Omarblack
Omarblack
OP
9
Original post by mqb2766
Good. Its worth noting that a venn diagram and that formula go hand in hand. The venn is used to visualize the data.

Yes, thanks for the help. Couldn't have done it without u!

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