Question

Hiro rolls a fair pair of six-sided dice. The sample space of all possible outcomes is shown below.

Let AAA be the event that the first die is one and BBB be the event that the sum of the dice is eight.
What is P(A\text{ or }B)P(A or B)P, left parenthesis, A, start text, space, o, r, space, end text, B, right parenthesis, the probability that the first die is one or the sum of the dice is eight?
\qquad

Answer 1

Answer:
`(11)/(36)`

Explanation:

Total outcomes for rolling a pair of six-sided dice n(S)= 6 x 6 =36

Let A be the event that the first die is one and B be the event that the sum of the dice is eight.

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

P(A)=
`=(n(A))/(n(S))=(6)/(36)`

B= {(2,6), (6,2), (3,5), (5, 3), (4,4)}

P(B)=
`=(n(B))/(n(S))=(5)/(36)`

A ∩ B = Ф

P(A ∩ B)=0

P(A or B)= P(A)+P(B)+P(A∩ B)

`=(6)/(36)+(5)/(36)+0\\=(11)/(36)`

Hence, P(A or B) =
`(11)/(36)`