Question

Q4. (12’) Morse code uses “dots” and “dashes”, which are known to occur in the proportion 3:4. Let D denote the event “a dot is sent”, and let ?̅ denote the event “a dash is sent”. Thus, we have P(D) = 3/7. When coded messages are sent, there can be errors in the transmission. Suppose that, with probability 1/10, a dot sent is erroneously received as a dash and vice-versa. If a dot is received, what is the probability that a dot was sent?

Answer 1

Here dots and dashes are to occur in proportion 3: 4

D = A dot is sent

= A dash is sen

P(D) = 3/7

P() = 4/7  

Here When code messages are sent, there can be errors in the transmission. with probability 1/10, a dot sent is erroneously received as a dash and vice-versa.

So here a dot was received.

A dot was received when a dot was sent and a dot was received or a dash was sent and a by an error a dot was received.

P(Dot Received) = P(D) * P(Correctly sent) + P() * P(Wrogly sent)

= 3/7 * 9/10 + 4/7 * 1/10 = 31/70

Now, we have to find

P(Dot was received when a dot was sent) = (3/7 * 9/10)/(31/70) = 27/31