Fridge Magnet Cereal

Probability question help, S1?

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.

1) The probability that the first two he gets are the same is 1 in 5 or 20%. The first one doesn't mater the second has a 1 in 5 chance of matching it.

2. Again, first magnet doesn't matter. The second has a 4/5 chance of being different to the first, the third has a 3/5 chance of being different again, the forth 2/5 and the fifth 1/5. Using percent that would be 80% * 60% *40%*20% that will equal 3.84%

3. 100% is the total so minus 3.84 from 100. Answer 96.16%

Technically all these probabilities are slightly off because there cannot be an unlimited supply of each.

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