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Two dice are rolled together. The probability of getting an outcome (a, b) such that b = 2a, is
Two dice are rolled together. The probability of getting an outcome (a, b)
such that b = 2a, is
a) 1/6
b) 1/12
c) 1/36
d) 1/9
This Question has 1 answers.
When two dice are rolled, the total number of possible outcomes is:
$6 \times 6 = 36$
We need to find the probability of getting an outcome $(a, b)$ such that $b = 2a$.
The possible values for $a$ and $b$ (both between 1 and 6) are:
- If $a = 1$, then $b = 2(1) = 2$ → Valid pair: $(1,2)$
- If $a = 2$, then $b = 2(2) = 4$ → Valid pair: $(2,4)$
- If $a = 3$, then $b = 2(3) = 6$ → Valid pair: $(3,6)$
- If $a = 4$, then $b = 2(4) = 8$ (not possible, since maximum value of $b$ is 6)
Thus, the valid pairs are:
$(1,2), (2,4), (3,6)$
Total favorable outcomes = 3
$\text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} $
$6 \times 6 = 36$
We need to find the probability of getting an outcome $(a, b)$ such that $b = 2a$.
The possible values for $a$ and $b$ (both between 1 and 6) are:
- If $a = 1$, then $b = 2(1) = 2$ → Valid pair: $(1,2)$
- If $a = 2$, then $b = 2(2) = 4$ → Valid pair: $(2,4)$
- If $a = 3$, then $b = 2(3) = 6$ → Valid pair: $(3,6)$
- If $a = 4$, then $b = 2(4) = 8$ (not possible, since maximum value of $b$ is 6)
Thus, the valid pairs are:
$(1,2), (2,4), (3,6)$
Total favorable outcomes = 3
$\text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} $
$= \frac{3}{36} = \frac{1}{12}$
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