Four bags, A, B, C and D each contains red discs and blue discs which are identical except for the colour.
Bag A contains 8 red discs and 2 blue discs.
Bag B contains 6 red discs and 4 blue discs.
Bag C contains 3 red discs and 5 blue discs.
Bag D contains 1 red discs and 7 blue discs.
(i) A disc is taken at random from A. Find, as a fraction, the probability that the disc is blue.
(ii) A disc is taken at random from B and another disc at random from C. Find, as a fraction, the probability that both discs are blue.
(iii) Two discs are taken at random from D. Find the probability that at least one of the discs is blue.
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Answer:
(i) P(Disc is blue)
= 2/(2 + 8)
= 2/10
=1/5
(ii) P(both discs are blue)
= P(disc from B is blue and disc from C is blue)
= 4/(6+4) * 5/(3+5)
= 4/10 * 5/8
= 1/4
(iii) P(at least one is blue)
= P(B,R) + P(R,B) + P(B,B)
= 7/8 * 1/7 + 1/8 * 7/7 + 7/8 * 6/7
= 1/8 + 1/8 + 6/8
= 1
