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conditional probability?

One Quater of the 800 pupils in the High School are in Sixth Form.
The probability that a pupil in the High School went to the local primary school is 2/5.
The probability that a Sixth Form pupil in the High School went to the local primary school is 1/10.
What is the probability that a pupil, not in the Sixth Form, went to a local primary school?
Reply 1
Avatar for Newton
Newton
Let event L be the event that a student chosen at random went to the local primary school.

Let event S be the event that a student chosen at random is in the sixth form.

=>P(L∩S')=P(L)-P(L∩S)

=>P(L∩S')=(2/5)-(1/10)=3/10

Newton.
Reply 2
Avatar for manps
manps
OP
seems unusally easy for 5 marks
Reply 3
Avatar for Jonny W
Jonny W
8
Newton
Let event L be the event that a student chosen at random went to the local primary school.

Let event S be the event that a student chosen at random is in the sixth form.

=>P(L ∩\cap S') = P(L) - P(L ∩\cap S)

=>P(L ∩\cap S')=(2/5)-(1/10)=3/10

P(L ∩\cap S)
= (1/4)(1/10)
= 1/40

P(L ∩\cap S')
= P(L) - P(L ∩\cap S)
= (2/5) - (1/40)
= 3/8

P(L | S')
= P(L ∩\cap S')/P(S')
= (3/8)/(3/4)
= 1/2

--

("Common sense" method".) Let p be the required probability and solve

(3/4)p + (1/4)(1/10) = 2/5

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