If two dice are thrown, then the probability | vedclass

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(A) When two dice are thrown, the total number of possible outcomes is $6^2 = 36$. Two numbers are coprime if their greatest common divisor $(GCD)$ is

Vedclass · Accepted Answer

$\frac{23}{36}$

Vedclass · Answer

(A) When two dice are thrown, the total number of possible outcomes is $6^2 = 36$. Two numbers are coprime if their greatest common divisor $(GCD)$ is $1$. It is easier to find the outcomes where the numbers are $NOT$ coprime (i.e.,$	ext{GCD} > 1$). The pairs $(x, y)$ where $	ext{GCD}(x, y) > 1$ are: $\{(2,2), (2,4), (2,6), (3,3), (3,6), (4,2), (4,4), (4,6), (5,5), (6,2), (6,3), (6,4), (6,6)\}$. The number of such outcomes is $13$. The number of favourable outcomes (where numbers are coprime) is $36 - 13 = 23$. Therefore, the required probability is $\frac{23}{36}$.

If two dice are thrown, then the probability of getting coprime numbers on the dice is

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