Question

Three boxes A, B and C, contain 100, 50 and 80 marbles of the same size respectively, some of which are black. In box A there are 15 black marbles. We select a box at random and then take a marble from that box, again at random. The probability to obtain a black marble this way is $\frac{101}{600}$. What is the greatest possible number of black marbles in box C?

Answer 1

Answer:

here is your answer mate...

Step-by-step explanation:

greatest possible number of black marbles in box C=15/60

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Answer 2

Answer:

22

Step-by-step explanation:

There are 15 black in box A.

Represent there are b black marbles in box B and c black marbles in box C.

We know that probability to select a box at random is 1/3 since there are 3 boxes, so P(a black marble) on A = 1/3*(15/100), on B = 1/3*(b/50) and on C = 1/3*(c/80).

Adding those 3 we will get:

1/3*(15/100 + b/50 + c/80) = 101/600

Next (15/100 + b/50 + c/80) = 101/200

Doing simplification will get

(8b + 5c)/400 = 71/200

Then 8b + 5c = 142.

You will get c maximum when b is minimum.

b minimum is 4

then 32 + 5c = 142

and will get c = 22

Conclusion: c maximum is 22.