Question

Two fairly six~sided dice are rolled,find the probability that their total score is (a)2 (b)7 (c)a prime number (d)a perfect square. Solutions. (a)2/6=1/3 (b)7/6

Answer 1

There are 36 ways for the 2 dice to fall
(make yourself a 6by6 matrix)

a)
there is only one way to get a sum of 2 ---> 1,1
prob (a sum of 2) = 1/36

b)
a sum of 7:
1 6, 2 5, 3 4, 4 3, 5 2, 6 1, so 6 ways
prob(a sum of 7) = 6/36 = 1/6

c) a prime:
the primes are 2, 3, 5, 7, or 11
number of ways to get a 2: 1
number of ways to get a 3: 2
number of ways to get a 5: 4
etc
prob(a prime) = 15/36
another way is to look at your matrix from above, and count how many prime numbers you see

d) count the perfect squares in your matrix
perfect squares possible are 4 and 9
I count 7of them
prob(perfect square as the sum) = 7/36