What is the probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 7?

Step-by-step explanation:

Let A and B represent the following events.

A = At least one of a pair of fair dice lands of 5

B = Sum of the dice is 7

It two dice are rolled then total number of outcomes is 36.

A = {(1,5),(2,5),(3,5),(4,5),(5,5),(6,5),(5,1),(5,2),(5,3),(5,4),(5,6)} = 11

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

A∩B = {(2,5),(5,2)}=2

We need to find the probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 7.

Therefore, the probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 7 is 1/3.

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116