Multiple choice

A box contains $10$ red marbles, $20$ blue marbles and $30$ green marbles, $5$ marbles are drawn at random. From the box, what is the probability that: At least one is green

  1. $\dfrac {4367}{4484}$
  2. $\dfrac {4671}{4484}$
  3. $\dfrac {467}{80004}$
  4. $\dfrac {437}{44684}$
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A Correct answer
Explanation

Total marbles = 60. Probability of drawing no green marbles is C(30, 5) / C(60, 5). Probability of at least one green is 1 - (C(30, 5) / C(60, 5)). Calculating this yields 4367/4484.

AI explanation

The box contains 60 marbles in total, including 30 green marbles, meaning there are 30 non-green marbles. The probability of at least one green marble is found by subtracting the probability of drawing zero green marbles from one. The ways to choose 5 non-green marbles from 30 is 30C5, and the total ways to choose any 5 marbles from 60 is 60C5, making the probability of zero green marbles 142506 divided by 5461512. Subtracting this from 1 gives a probability of 5319006 divided by 5461512, which simplifies to 4367 divided by 4484.

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