Question

A bag contains 9 blue marbles and 3 red marbles. You draw three marbles without replacement. What is the probability of drawing three blue marbles?

21⁄55 = 38.2%

6⁄11 = 54.5%

7⁄24 = 29.2%

56⁄81 = 69.1%

243⁄440 = 55.2%

Answer 1

Answer: The answer is A 21/55

Explanation:

Answer 2

Let's see what's happening with each extraction, in terms of favourable cases vs total cases:

With the first extractions, you have 12 marbles, and 9 of them are blue. The probability of extracting a blue one is thus

`\cfrac{9}{12} = \cfrac{3}{4}`.

With the second extractions, you have 11 marbles (we don't replace the first one!), and 8 of them are blue (we already picked one!). The probability of extracting a blue one is thus

`\cfrac{8}{11}`.

Finally, you have 10 marbles, and 7 of them are blue (we already picked two!). The probability of extracting a blue one is thus

`\cfrac{7}{10}`.

If you want events to happen one after the other, you have to multiply their probabilities, so the answer is

`\cfrac{3}{4} \cdot \cfrac{8}{11} \cdot \cfrac{7}{10} = \cfrac{168}{440} = \cfrac{21}{55}`