Question

Consider the experiment where a pair of fair dice is thrown. Let X denote the random variable whose value is determined by taking the maximum of the spots showing on either of the two dice thrown. For example, if a 3 and a 5 were thrown, then X would take the value of Maximum(3,5) = 5. The range of values that X can assume are the positive integers {1,2,3,4,5,6}.
1. Please give the corresponding probabilities for the values of X given below.
Pr(X = 1) =
Pr(X = 2) =
Pr(X = 3) =
Pr(X = 4) =
Pr(X = 5) =
Pr(X = 6) =
2. Further, find the probability that X is divisible by 4. Probability that X is divisible by 4 = ______

Answer 1

Answer:

1-

P(X=1) = 1/36

P(X=2) = 3/36 = 1/12

P(X=3) = 5/36

P(X=4) = 7/36

P(X=5) = 9/36 = ¼

P(X=6) = 11/36

2-

7/36

Step-by-step explanation:

1-

Attached, you will find a table with the possible values of X.

(See table attached)

As we can see, there are 36 entries so,

P(X=1) = 1/36

P(X=2) = 3/36 = 1/12

P(X=3) = 5/36

P(X=4) = 7/36

P(X=5) = 9/36 = ¼

P(X=6) = 11/36

2-

It can be noticed that the only possible value of X which is divisible by 4 is 4 and there are 7 entries in the table, so

P(X divisible by 4) = P(X=4) = 7/36