First slide

Theorems of probability

Question

Two persons each makes a single throw with a pair of dice. The probability that their scores are equal is

Moderate

A

65/648
B

69/648
C

73/648
D

98/648

Solution

$Total number of cases = n (S) = (6^{2}) (6^{2}) = 36^{2}$
$For favorable cases n (E)$
$Their scores can be 2, 3, 4, \dots, 12$
$Number of cases in which both score '2' or '12' is 1 \times 1$
$Number of cases in which both score '3' or '11' is 2 \times 2$
$Number of cases in which both score '4' or ' 10' is 3 \times 3$
$Number of cases in which both score '5' or '9' is 4 \times 4$
$Number of cases in which both score ' 6' or ' 8' is 5 \times 5$
$Number of cases in which both score '7' is 6 \times 6$
$\begin{matrix} ∴ Required probability, n (E) = \frac{2 (1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2}) + 6^{2}}{(36)^{2}} \\ = \frac{73}{648} \end{matrix}$

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