Question

TO CLARIFY: I am confused about part b) of the problem.

a) A display case contains thirty-five gems, of which ten are real diamonds and twenty-five are fake diamonds. A burglar removes four gems at random, one at a time and without replacement. What is the probability that the last gem she steals is the second real diamond in the set of four?

b) Then, suppose that the burglar removes 10 diamonds instead. How many real diamonds is she more likely to steal?

Answer 1

b)

Out of 35 , 10 are real gems

P[ A gem is real ] = 10/35

P[ A gem is real ] = 2/7

Now, she steal 10 gems

n = 10

Number of real gems she is most likely to have = average number of real gems in a pick of 10

Number of real gems she is most likely to have = 10*(2/7)

Number of real gems she is most likely to have = 10*0.2857

Number of real gems she is most likely to have = 2.857

Number of real gems she is most likely to have = 3 gems