When coded messages are sent, there are sometimes errors in transmission. In particular, Morse code uses "dots" and "dashes," which are known to be sent in the proportion 3:4. This means that for any given symbol, P(dot sent) = 3/7, and P(dash sent) = 4/7. Suppose there is interference on the transmission line, and with probability 1/8 a dot sent is mistakenly received as a dash; in other words, P(dash received | dot sent) = 1/8. Also suppose that due to interference, there is probability 1/8 that a dash sent is mistakenly received as a dot; in other words, P(dot received | dash sent) = 1/8. When we receive a dot in the transmission, how confident can we be that it really was a dot that was sent? In other words, what is the posterior probability P(dot sent | dot received)?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
When coded messages are sent, there are sometimes errors in transmission. In particular, Morse code uses "dots" and "dashes," which are known to be sent in the proportion 3:4. This means that for any given symbol, P(dot sent) = 3/7, and P(dash sent) = 4/7.
Suppose there is interference on the transmission line, and with probability 1/8 a dot sent is mistakenly received as a dash; in other words, P(dash received | dot sent) = 1/8. Also suppose that due to interference, there is probability 1/8 that a dash sent is mistakenly received as a dot; in other words, P(dot received | dash sent) = 1/8.
When we receive a dot in the transmission, how confident can we be that it really was a dot that was sent? In other words, what is the posterior probability P(dot sent | dot received)?
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