Amodem transmits over an error-prone channel, so it repeats every "0" or "1" bit transmission five times. we call each such group of five bits a "codeword." the channel changes an input bit to its complement with probability p =1/10 and it does so independently of its treatment of other input bits. the modem receiver takes a majority vote of the five received bits to estimate the input signal. find the probability that the receiver makes the wrong decision.

0.00111

Step-by-step explanation:

Since the modem receiver takes a majority vote of the five

received bits to estimate the input signal, it will only make a wrong decision if 3, 4 or 5 of the 5 bits received are wrong.

Given that the channel changes an input bit to its complement with probability p =1/10 and it does so independently of its treatment of other input bits, the probability of changing 3 bits out of five is 0.1*0.1*0.1 = 0.001, of changing 4 is 0.0001 and of changing 5 is 0.00001

So, the probability that the modem makes a wrong decision is 0.001+0.0001+0.00001 = 0.00111

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1