In a single throw of 3 dice,find the probabil | vedclass

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(A) The total number of outcomes when throwing $3$ dice is $6^3 = 216$.$A$ total of at most $5$ means the sum of the numbers on the $3$ dice is $3, 4,

Vedclass · Accepted Answer

$\frac{5}{108}$

Vedclass · Answer

(A) The total number of outcomes when throwing $3$ dice is $6^3 = 216$.$A$ total of at most $5$ means the sum of the numbers on the $3$ dice is $3, 4,$ or $5$.Cases for a total of $3$: $(1, 1, 1)$ - $1$ case.Cases for a total of $4$: $(1, 1, 2), (1, 2, 1), (2, 1, 1)$ - $3$ cases.Cases for a total of $5$: $(1, 1, 3), (1, 3, 1), (3, 1, 1), (1, 2, 2), (2, 1, 2), (2, 2, 1)$ - $6$ cases.Total favourable cases = $1 + 3 + 6 = 10$.Therefore,the probability of getting a total of at most $5$ is $\frac{10}{216} = \frac{5}{108}$.

In a single throw of $3$ dice,find the probability of getting a total of at most $5$.

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