Respuesta :
Answer:
0.8432
Step-by-step explanation:
The probability of a correct transmission of individual character = 0.9
Let's consider the three possible scenarios:
1) Probability of all 14 characters transmitted correctly = 0.9^14 = 0.2287
2)Probability of only one character being wrong: (0.9 ^ 13) * 0.1
This equals 0.02541 To account for the order at which the incorrect character is produced, lets consider the permutation: [tex]\frac{14!}{13!*1!}[/tex]
This accounts for same objects or results being repeated, and is an integral part of permutation questions. The result is 14. Thus there are 14 ways for the probability of 0.02541 to occur. That means a total of 0.02541 * 14 probability. This equals 0.3559
3) Probability of both characters being wrong:
Similar steps to (2). Probability = (0.9^12) * (0.1 ^ 2) =0.002824
Number of ways this could occur: [tex]\frac{14!}{12!*2!}[/tex] = 91
Total probability for this event: 0.002842 * 91 = 0.2586
The answer to our question is thus all these probabilities combined, which makes: 0.2287 + 0.3559 + 0.2586 = 0.8432
It can be deduced that probability that a message transmitted using this code will be correctly received will be 0.8432.
How to calculate the probability
From the given information, there are Hamming code of length 14 that corrects 2 errors.
The probability that all the characters will be transmitted correctly will be 0.2287. The probability of one event being wrong is 0.3559 and the probability of both to be wrong will be 0.2586.
Therefore, the probability that a message transmitted using this code will be correctly received will be the addition of all the values. This will be:
= 0.2286 + 0.3559 + 0.2586
= 0.8432
In conclusion, the correct option is 0.8432.
Learn more about probability on:
https://brainly.com/question/25870256
