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A box of chocolates is randomly selected from a production line to check to see if any of the chocolates are faulty. Each box contains 12 chocolates with soft-centres and 8 with hard-centres. Two chocolates are randomly selected from the box and are tested to see if they have any faults.

a) Calculate the probability of selecting two soft-centered chocolates.
b) Calculate the probability of selecting a soft-centred and a hard-centred chocolate (not in any particular order).
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A box of chocolates is randomly selected from a production line to check to see if any of the chocolates are faulty. Each box contains 12 chocolates with soft-centres and 8 with hard-centres. Two chocolates are randomly selected from the box and are tested to see if they have any faults.

a)    P(two soft-centered chocolates) = (12/20) x (11/19) = 33/95 = 0.347.. = 0.35

b)    P(soft-centred and hard-centred chocolate) = P(S and H, or H and S) = P(S, H) + P(H, S) = (12/20)x(8/19) + (8/20)x(12/19) = 48/95
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