MCQ
Two dice are thrown together. The probability of getting a doulet is :
- A$\frac{1}{3}$
- ✓$\frac{1}{6}$
- C$\frac{1}{4}$
- D$\frac{2}{3}$
✓
Answer
Correct option: B.
$\frac{1}{6}$
The number on each die are $\{1, 2, 3, 4, 5\}$ and $6.$
So, the total possibilities are :
$\{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)\}$
$\{(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)\}$
$\{(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)\}$
$\{(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)\}$
$\{(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)\}$
$\{(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)\}$
So, there are $36$ number in toral.
There are 6 possibilities when we obtain a doublet,
$\{(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)\}.$
$P($getting a doublet$)$
$=\frac{6}{36}$
$=\frac{1}{6}$
So, the total possibilities are :
$\{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)\}$
$\{(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)\}$
$\{(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)\}$
$\{(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)\}$
$\{(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)\}$
$\{(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)\}$
So, there are $36$ number in toral.
There are 6 possibilities when we obtain a doublet,
$\{(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)\}.$
$P($getting a doublet$)$
$=\frac{6}{36}$
$=\frac{1}{6}$
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