Probability Mass Function - Coin and Die

Let m represent the upturn of a fair coin (head = 1 and tail = 0) and n signify the uptrun of a fair die. Compute, by using a box, the probability mass function for B = (3m + n).

Tan said:

Let m represent the upturn of a fair coin (head = 1 and tail = 0) and n signify the uptrun of a fair die. Compute, by using a box, the probability mass function for B = (3m + n).

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Tan, you need to know that B has nine outcomes: 1,2,3,…,8,9.
There are six of those, 1,2,3,7,8,9, that happen only in one way.
For example, B=3 if m=0 & n=3 so P(B=3)=(1/2)(1/6).

The values, 4,5,6 can each happen in two ways.
For example, B=5 if m=0 & n=5 or m=1 & n=2 so P(B=5)=(1/2)(1/6)+(1/2)(1/6).

Now you complete the PMF.