Answer
The probability of selecting all the red ones is equal to $\frac 8 {792}$.
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 red ones: $C(4,4) = 1$
We have already selected 4. We have to pick another one to select a total of 5:
- Select a random non-red one: $C(8,1) = 8$
$n(E) = 1 \times 8 = 8$
3. Find the probability:
$P(E) = \frac{n(E)}{n(S)} = \frac 8 {792} $
