Answer
The probability of selecting all the green ones is equal to $\frac {36} {792}$.
Work Step by Step
1. Calculate the number of elements in the sample space $S$:
From a bag containing 12 balls, you select 5 at random, thus:
$n(S) = C(12,5) = 792$
2. Calculate the number of elements in the event $E$:
- Select all the green marbles: $C(3,3) = 1$
We have already selected 3. We have to pick 2 more balls to select a total of 5:
- Select two random non-green ones: $C(9,2) = 36$
$n(E) = 1 \times 36 = 36$
3. Find the probability:
$P(E) = \frac{n(E)}{n(S)} = \frac {36} {792} $
