We roll two fair 6-sided dice. (If a fair dice is rolled, the probability of it

Question

We roll two fair 6-sided dice. (If a fair dice is rolled, the probability of it landing on any number between [1-6] is equi-probable.) Find the probability that doubles are rolled. (Rolling doubles mean both dices land in the same number, e.g., 3 and 3.) Given that the roll results in a sum of 6 or less, find the conditional probability that doubles are rolled. Find the probability that the larger of the two die's outcomes is at least 4. Given that the two dice land on different numbers, find the conditional probability that at least one die roll is a 1. Let X be the event that the first die results in an odd number, and Y be the event that the rolled sum is an even number. Compute Pr[X], Pr[Y], Pr[X Y]. Are X and Y independent? Let X be the event that the first die results in a multiple of 2, and Y be the event that the rolled sum is a multiple of 2. Compute Pr[X], Pr[Y], Pr[X F]. Are X are Y independent? Let X be the event that the first die results in a multiple of 3, and Y be the event that the rolled sum is a multiple of 2. Compute Pr[X|Y] and Pr[Y|X]. Are X are Y independent?

Explanation / Answer

A) Total number of outcomes = 36

Number of doubles = 6

P(double) = 6/36 = 1/6

B) No of results with sum 6 or less = 5+4+3+2+1 = 15

No of doubles when sum is 6 or less = 3

P(double | sum is 6 or less) = 3/15 = 1/5

C) Number of cases where larger of the two die's outcome is at least 4 = 36-9 = 27

P(larger of the two die's outcome is at least 4) = 27/36 =3/4

D) No of cases in which numbers are different = 36-6 = 30

No of 1s in such cases = 10

P(one die roll is 1 when the numbers are different) = 10/30 = 1/3

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

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