Question

Two different dice are thrown together.i) find the probability of getting a number greater than 3 on each side

Answer 1

total no. in two dice
$= 6 + 6 = 12$
total no. of pairs which can be arranged in 2 dice
$= 6 \times 6 = 36$
no.s greater than 3 in two dice
$= 4 \\ = 5 \\ = 6 \\ = 7 \\ = 8 \\ = 9 \\ = 10 \\ = 11 \\ = 12$
chances of getting 4
$2 + 2 \\ 3 + 1 \\ 1 + 3 \\ \\ = 3 \: chances$

chances of getting 5
$4 + 1 \\ 1 + 4 \\ 3 + 2 \\ 2 + 3 \\ \\ total \: chances \: of \: 4 \: n \: 5 = 7$
chances of getting 6
$3 + 3 \\ 4 + 2 \\ 2 + 4 \\ 5 + 1 \\ 1 + 5 \\ \\ total \: chances \: \\ = 12 \: including \: all$
chances of getting 7
$4 + 3 \\ 3 + 4 \\ 5 + 2 \\ 2 + 5 \\ 6 + 1 \\ 1 + 6 \\ \\ total = 5 + 12 = 18$
chances of getting 8
$2 + 6 \\ 6 + 2 \\ 3 + 5 \\ 5 + 3 \\ 4 + 4 \\ \\ total = 18 + 5 = 23$

chances of getting 9
$5 + 4 \\ 4 + 5 \\ 6 + 3 \\ 3 + 6 \\ \\ total = 23 + 4 = 27$
chances of getting 10
$5 + 5 \\ 4 + 6 \\ 6 + 4 \\ \\ total = 27 + 3 = 30$
chances of getting 11
$6 + 5 \\ 5 + 6 \\ \\ total = 2 + 30 = 32$
chances of getting 12
$6 + 6 \\ \\ total = 32 + 1 = 33$

probability =
(total no. of no greater than 3)/(total no)
= 33/36 answer