Question

A network of 8 computers is connected to another network of 5 computers by a central hub. If a message needs to be sent between the two networks of computers, it must pass through the central hub. A message is produced in a randomly selected computer in either network; then,  that first computer sends the message to a second randomly selected computer (different than the first) in either network; then, that second computer sends the message to a third randomly selected computer (different than the first two computers) in either network. Find the probability that the message passes through the central hub at least once.

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Answer 1

Probability that the message passes at least once through central hub-

$=1-P(\text{ No message is pass through central hub)}$

$=1-\dfrac{^8C_1.^5C_1}{^{13}C_2}$

$=1-\dfrac{8(5)}{78}$

$=1-\dfrac{40}{78}=\dfrac{38}{78}=0.4871$