Question

What is probability of getting the sum as a prime number when two dice sre thrown?

Answer 1

total numbers in two dice
$= 6 + 6 = 12$

prime numbers in two dice
$2 \\ 3 \\ 5 \\ 7 \\ 11$


chances of getting 2

$= 1 + 1$
chances of getting 3

$= 2 + 1 \\ = 1 + 2$



chances of getting 5
$= 1 + 4 \\ = 4 + 1 \\ = 3 + 2 \\ = 2 + 3$
chances of getting 7
$= 4 + 3 \\ = 3 + 4 \\ = 5 + 2 \\ = 2 + 5 \\ = 6 + 1 \\ = 1 + 6$
chances of getting 11
$= 6 + 5 \\ = 5 + 6$
therefore total outcome of prime no. =15 (ways)
and total no. of all outcome = 6×6 =36
(how many times 2 dice's no. can be arranged)




$probability = \frac{total number \: of \: outcome \: of \: prime \: no.}{total \: no. \: of \: outcome} \\ \\ = \frac{15}{36} \\ \\ = \frac{5}{12}$








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