A communication system uses three frequencies, (denote it as F1, F2; and F3); because bad weather can cause the loss of the use of one or more frequencies. Suppose there is a loss of 10% of exactly one frequency, a loss of 1% of exactly two frequencies, and a loss of 0:5% of exactly three frequencies. Define a normal mode of operation when at least two frequencies are working and an emergency mode of operation when at least one frequency is working. Define the event when the system is working as OK.

a. Find P[OK in emergency mode].
b. Find P[OK in normal mode].

Hint: This sample space has 8 sample points. Find their associated probabilities and then you should be able to do the problem.