Answer
The total number of outcomes is equal to 6. $n(S) = 6$
The element of the event $E$ is: $E = \{2\}$
Probability of rolling a 2 is equal to $\frac 1 8$
Work Step by Step
- The numbers that can come up are: 1, 2, 3, 4, 5 and 6. Therefore, there are 6 elements in the sample space.
$n(S) = 6$
1. Label the unknowns:
x = Probability of rolling a 2, 3, 4 or 5.
y = Probability of rolling a 1 or 6.
2. According to the exercise, $x$ is half of $y$, so:
$\frac{1}{2}y =x$ or $2x = y$
3. The sum of all probabilities must be equal to 1:
Respectively, probability of rolling a 1, 2, 3, 4, 5 or a 6:
$y + x + x + x+ x+ y = 1$
- Substituting:
$2x + x + x + x +x + 2x = 1$
$8x = 1$
$x = \frac 1 8$
4. The event is: rolling a 2, so the set is:
$E = \{2\}$
5. Since the probability of 2 coming up is equal to "x", we already have the answer.
Probability of rolling a 2 : $\frac 1 8$
