hi i'm a bit confused on a simple question which i thought i did correct, but the mark scheme has a different answer.
A bag contains a large number of coins:
75% are 10p coins,
25% are 5p coins.
A random sample of 3 coins is drawn from the bag.
Find the sampling distribution for the median of the values of the 3 selected coins
and the answer is:
Median 5: p = (0.25)^3 + 3(0.75)(0.25)^2 = 10/64
Median 10: p = (0.75)^3 + 3(0.25)(0.75)^2 = 54/64
so basically they are using the case for median 5 with 2 5's or 3 5's, but these are the combinations:
Median 5: (5 5 5) (5 5 10) (10 5 10) (10 5 5)
Median 10: (10 10 10) (5 10 10) (10 10 5) (5 10 5)
why are the combinations i've shown in red used the other way around?
the combination (10 5 10) have median 10. For getting the median, the first step we have to order from low to higher. The combination (5, 10 5) have median 5.
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