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### Question

A box contains 6 cyan, 3 pink and 8 orange marbles. What is the probability of drawing a orange marble if 2 marbles are drawn out randomly?

**A**

${25/34}$.

**B**

$8/17$.

**C**

$26/136$.

**D**

$30/136$.

**Soln.**

**Ans: a**

Total number of marbles is 17. Combinations of 2 marbles that are possible = ^{17}C_{2} = ${17 × 16}/2$ = 136. If one of the two balls is orange, then both balls will be orange in ^{8}C_{2} = ${8 × (8 - 1)}/2$ = 28 ways. The number of ways in which non-orange can be drawn out are 8 × (6 + 3). So total favorable outcomes = 28 + 8 × 9 = 100, and the probability is 100/136 = ${25/34}$.