You are rolling two unbiased dice, one red and one blue, and recording the order

Question

You are rolling two unbiased dice, one red and one blue, and recording the ordered pair(spots up on red die,spots up on blue die). Determine the possible outcomes of this experiment. if the results on the dice are independent, determine the probabilities of the following events:

a) a 1 on the red die;

b) a 1 on each die;

c)a 1 on at least one of the 2 dice;

d)the sum of the two values equals 7;

e)the sum of the two values is an even number

f)the number on the blue die is at least as large as the number on the red die;

g)getting equal numbers on the two dice.

Please answer and explain :)

Explanation / Answer

a) 1/6: The outcome is independent of blue die and probability of getting 1 on a single die is 1/6

b) 1/36 : out of the 36 possible outcomes, only possible answer is(1,1) so probability is 1/36

c) 11/36: (1,1), (1,2), (1,3), (1,4)....(1,6) and (2,1), (3,1),.....(6,1)

d) 6/36=1/6: (6,1), (1,6), (5,2), (2,5), (4,3), (3,4)

e) 1/2: (1,1), (1,3), (1,5), (2,2) (2,4), (2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)

alternate solution: either the sum is even or odd and probability of getting both of them is same

f) 21/36=7/12: If red die has 1 then blue die can contain all six outcomes that are equal to or larger than 1

If red die has 2 then blue die can have five outcomes that are equal or larger than 2

Similarly, the same is case with the rest and outcomes are 6+5+4+3+2+1=21

g) 6/36=1/6: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

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