Mrs. Rayne has a phone tree to contact all of her family in the case of an emergency. She

calls the first two family members and then those family members call two family members

each and each of those family members calls two family members. If the pattern continues

how many family members are contacted on the 3rd round?

In the third round, total family members contacted is 8.

Step-by-step explanation:

Let us assume that Mrs Rayne contacts two members in her family say A and B

or, Total new members contacted in First Round = A and B (2 members)

Now, in second Round, A contacts two members say H and G

and B contacts L and M

So, Total new members contacted in second round = H, G, L and M (4)

Now, in third round each of the members H, G, L and M contact two people each say

H contacts W, X

G contacts Y, Z

L contacts P, Q

and M contacts R and S

So, Total new members contacted in second round = W, X, Y, Z, P, Q R and S

Hence, in the third round, total family members contacted is 8.

In the third round, total family members contacted is 8.