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S2 june 2010 question need help, probabilities please help!!! Watch

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    Each packet of cruncho cereal contains one free fridge magnet. There are five different types of fridge magnet to collect. They are distributed, with equal probability, randomly and independently in the packets. Keith is about to start collecting these fridge magnets.

    i) Find the probability that the first 2 packets that Keith buys contains the same type of fridge magnet.

    ii) Find the probability that Keith collects all five types of fridge magnets by buying just five packets .

    iii) Hence find the probability that Keith has to buy more than five packets to acquire a complete set.
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    i) For the first packet we don't care what magnet we get but for the second packet, we want to get the same magnet as the one we already have. The probability of this happening is 1/5.

    ii) For the first packet we don't care what magnet we get, for the second packet we want one of the 4 out of 5 magnets we don't already have, for the third packet we want one of the 3 out of 5 magnets we don't already have, etc. Calculate the probability of us getting a magnet we're happy with in each packet and multiply those probabilities together.

    iii) We certainly need at least 5 packets to get a complete set so we either buy 5 packets or we buy more than 5 packets. We buy more than 5 packets if we don't get the magnets we want in the 1st five packets. The probability of this happening is 1 minus the probability of getting 5 different magnets in the first 5 packets.
 
 
 
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