Question

When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below.
(1.1) (1.2) (1,3) (1.4) (1,5) (1.6)
(2.1) (2.2) (2,3) (2.4) (2.5) (2,6)
(3.1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4.1) (4.2) (4.3) (4.4) (4.5) (46)
(5.1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6.1) (6,2) (63) (6,4) (6,5) (6, 6)
Let X denote the smaller of the two numbers. If both dice come up the same number, then X
equals that common value. Find the probability distribution of X. Leave your probabilities in
fraction form

Answer 1

Answer:

1=11/36, 2=9/36, 3=7/36, 4=5/36, 5=3/36, 6=1/36

Step-by-step explanation:

If a 1 is rolled, there is a 6/6 chance of a 1 being the lowest. If a 2 is rolled, there is a 5/6 chance of a 2 being the lowest, and a 1/6 chance of a 1 being the lowest.  If a 3 is rolled, there is a 4/6 chance of a 2 being the lowest, a 1/6 chance of a 2 being the highest, and a 1/6 chance of being the lowest. etc.