Question

A pair of dice is rolled, and the sum of the numbers is either 7 or 11. What is the probability of this event?

Answer 1

Probability that sum of numbers is either 7 or 11 is:

0.22

Explanation:

A pair of dice is rolled.

Sample Space:

(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)

Total outcomes= 36

Outcomes with sum of numbers either 7 or 11 are in bold letters=8

i.e. number of favorable outcomes=8

So, P(sum of numbers is either 7 or 11 )=8/36

=0.22

Answer 2

Answer:
`(2)/(9)`

Explanation:

Let A be the event that the sum is 7 and and B be the event that the sum is 11 .

When two pair of dices rolled the total number of outcomes =
`n(S)=6*6=36`

The sample space of event A ={(1,6), (6,1), (5,2), (2,5), (4,3), (3,4)}

Thus n(A)= 6

The sample space of event B = {(5,6), (6,5)}

n(B)=2

Since , both the events are independent , then the required probability is given by :-

`P(A\cup B)=P(A)+P(B)\\\\=(n(A))/(n(S))+(n(B))/(n(S))=(6)/(36)+(2)/(36)=(8)/(36)=(2)/(9)`

Hence, the required probability =
`(2)/(9)`