3. You have a single interesting die; it has a 1 on 3 sides and a 0
on the other 3 sides. The die is rolled three times –
what is the probability that a 1 will appear -
a. Exactly twice out of three rolls? Do this by TWO METHODS
1.) use the brute force (relative frequency, i.e., list all possible combinations and use these results to determine the answer),
2.) use Bernoulli Trials (Binomial Random Variable).
b. At least twice out of three rolls? Repeat as per Part a above.

4. In a digital communications system, messages are encoded
into the binary symbols 1 and 0, and because of noise
in the system, sometimes the signal sent is not the signal received,
e.g., a 1 is sent but a 0 was received. The probability of
0 being transmitted is 0.2 and the probability of a 1
being transmitted is 0.8. Also, it is known that the probability of
a 0 being received as a 1 is 0.02 and the probability of
a transmitted 1 being received as a 0 is 0.01.
a.Given that a 0 was transmitted what is the probability that a 0 was received?
b.Given that a 1 was transmitted what is the probability that a 1 was received?
c.What is the probability that either symbol is received in error?