A pair of dice is loaded. The probability that a 4 appears on the first die is 2/7, and the probability that a 3 appears on the second die is 2/7. Other outcomes for each die appear with probability 1/7. What is the probability of 7 appearing as the sum of the numbers when the two dice are rolled?

9/49

Step-by-step explanation:

For the first die, probability of obtaining 4 = 2/7

For the second die, the probability of obtaining 3 = 2/7

Other outcomes for each die appear with a probability of 1/7

There are six cases of obtaining the sum of the two die as 7.

E1 = 1 and 6

E2 = 2 and 5

E3 = 3 and 4

E4 = 4 and 3

E5 = 5 and 2

E6 = 6 and 1

Pr (E1) = 1/7*1/7

= 1/49

Pr (E2) = 1/7*1/7

= 1/49

Pr (E3) = 1/7*1/7

= 1/49

Pr (E4) = 2/7*2/7

= 4/49

Pr (E5) = 1/7*1/7

= 1/49

Pr (E6) = 1/7*1/7

= 1/49

P (E) = Pr (E1) + Pr (E2) + Pr (E3) + Pr (E4) + Pr (E5) + Pr (E6)

= 1/49 + 1/49 + 1/49 + 4/49 + 1/49 + 1/49

= 9/49