probability help (5m)

1) Possible events:

1 + 7, 2 + 6 and 3 + 5

each having a probability of 2/6 x 1/5 = 1/15

So total probability = 3 x 1/15 = 1/5

2) P(No '1' occurs) = 5/6 x 5/6 = 25/36

Hence P(At least one '1' occurs) = 1 - 25/36 = 11/36

3) Possible events to make the sum smaller or equal to 4:

1 + 1, 1 + 2, 2 + 1, 3 + 1, 1 + 3, 2 + 2

each having a probability of 1/36

Hence P(Sum <= 4) = 1/6

P(Sum > 4) = 5/6

4) The centre of the coin should be at least 1 cm away from any edge of a tile, hence the probability is:

(10 - 2 x 1)2/102 = 32/50