conditional probability? Watch

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manps
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#1
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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?
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Newton
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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.
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manps
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seems unusally easy for 5 marks
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Jonny W
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(Original post by 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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