Two 6-sided dice are tossed. One die is red and the other is white, so that they

Question

Two 6-sided dice are tossed. One die is red and the other is white, so that they are distinguishable. (That is, we consider the pair of numbers (number showing on red die, number showing on white die), for example, one outcome is (3, 1), which is different from (1, 3).). Let A be the event that the sum of the dice is even, B be the event that at least one die shows a 3 and C be the event that the sum of the dice is 7. Identify the elements of: (a) A Intersection B (b) B^c Intersection C (c) A Intersection C (d) A^c Intersection B^c Intersection C^c

Explanation / Answer

(a) If the white die shows 3, the red die must show 1,3 or 5 for the sum to be even.

Thus A B = {(1,3),(3,3),(5,3),(3,1),(3,5)}

(b) Bc is the event where neither die shows 3.

Thus Bc C = {(1,6),(2,5),(5,2),(6,1)}

(c) Since A wants the sum to be even and C needs the sum to be 7 which is odd,

A C =

(d) Ac is the event where the sum of the dice is odd. Cc is the event where the sum of the dice is not 7.

Thus Ac Cc needs the sum to be 3,5,9,11.

Further Bc does not allow a 3 on either die.

Ac Bc Cc = {(1,2),(2,1),(1,4),(4,1),(4,5),(5,4),(5,6),(6,5)}

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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