A certain brand of boxes of matches is advertised as having "average contents 50 matches". The probability that a box chosen at random will contain exactly 50 matches is 5/8.
(a) Calculate the probability that a box of matches chosen at random will not contain exactly 50 matches.
The probability that a box chosen at random will contain more than 50 matches is twice the probability that it will contain less than 50 matches.
(b) Calculate the probability that
(i) one box chosen at random will contain at least 50 matches.
(ii) of 2 boxes chosen at random, at least one will contain less than 50 matches.
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Answer:
(a) P(a box of matches chosen at random will not contain exactly 50 matches)
= 1 - 5/8
= 3/8
(b)
The probability that a box chosen at random will contain more than 50 matches is twice the probability that it will contain less than 50 matches
====> P(a box chosen at random will contain more than 50 matches) = 2/8
====> P(a box chosen at random will contain less than 50 matches) = 1/8
(i) P(one box chosen at random will contain at least 50 matches)
= P(a box chosen at random will contain more than 50 matches) + P((a box chosen at random will contain exactly 50 matches)
= 2/8 + 5/8
= 7/8
(ii) P(at least one will contain less than 50 matches)
= 1 - P(both boxes contain at least 50 matches)
= 1 - 7/8 * 7/8
= 15/64
