(1 point) Consider the experiment where a pair of fair dice is thrown. Let X den

Question

(1 point) 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 18 Probability that X is divisible by 18 equals

Explanation / Answer

Solution:-) The sample space for rolloing a two die and as the total is 6 . Each outcome will have probability 1/36(say n). The sample space will be

S= {(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), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

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.

P(X=1)= 1/36

P(X=2)= 2/36

P(X=3)= 2/36

P(X=4)= 3/36

P(X=5)= 2/36

P(X=6)= 4/36

P(X=8)= 2/36

P(X=9)= 1/36

P(X=10)= 2/36

P(X=12)= 4/36

P(X=15)= 2/36

P(X=16)= 1/36

P(X=18)= 2/36

P(X=20)=2/36

P(X=24)=2/36

P(X=25)=1/36

P(X=30)=2/36

P(X=36)=1/36

b) The numbers that are divisible by 18 are 18 itself and 36. which will came from

(6,3)(3,6)(6,6)

Probability that X is divisible by 18 equals to 3/36

CHEERS!!

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

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