Curious die, probability/stats

Question

A peculiar die has the following properties: on any roll the probability of rolling either a 4, a 3, or a 2 is 1/2, just as it is with an ordinary die. Moreover, the probability of rolling either a 2, a 1, or a 6

 is again 1/2. However, the probability of rolling a 2 is 5/16, not 1/6 as one would expect of an ordinary fair die.

From what you know about this peculiar die, compute the following.

1. The probability of rolling anything but a 2
2. The probability of rolling a 5

Answer 1

Prob(2) = 5/16

Prob(2,3,4) = 1/2 = 8/16 ---> Prob(3 or 4) = 8/16 - 5/16 = 3/16 ---> prob(3) = 3/32 = prob(4)

Prob(1,2,6) = 1/2 = 8/16 ---> Prob(1,6) = 8/16 - 5/16 = 3/16 ---> prob(1) = 3/32 = prob(6)

prob(1) = 3/32

prob(2) = 5/16 = 10/32

prob(3) = 3/32

prob(4) = 3/32

prob(5) = 10/32 = 5/16

prob(56) = 3/32

prob( not 2) = 22/32 = 11/16