Consider the experiment where a pair of fair dice is thrown. Let X denote the ra

Question

Consider the experiment where a pair of fair dice is thrown. Let X denote the random variable whose value is determined by multiplying the number of spots showing on the one die by the number of spots showing on the other. The range of values that X can assume are the positive integers {1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,30,36}. 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) = Pr(X = 8) = Pr(X = 9) = Pr(X = 10) = Pr(X = 12) = Pr(X = 15) = Pr(X = 16) = Pr(X = 18) = Pr(X = 20) = Pr(X = 24) = Pr(X = 25) = Pr(X = 30) = Pr(X = 36) = Further, find the probability that X is divisible by 4. Probability that X is divisible by 4 equals ?????

Explanation / Answer

The easiest is when X = 6. there's only one way that will happen: if both dice give a 6, which is a 1/36 chance.

For X = 5, you're looking at either (5,5), (5,6), or (6,5), so 3/36.

X = 4: (4,4), (4,5), (4,6), (5,4), (6,4), so 5/36.

Continue in this fashion for all the others. Once you've calculated the probabilities for X=2,3,4,5, and 6, you can add them up and subtract the total from 1 to find P(X=1).

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.