Answer:
The probability that the message will be wrong when decoded is 0.05792
Step-by-step explanation:
Consider the provided information.
To reduce the chance or error, we transmit 00000 instead of 0 and 11111 instead of 1.
We have 5 bits, message will be corrupt if at least 3 bits are incorrect for the same block.
The digit transmitted is incorrectly received with probability p = 0.2
The probability of receiving a digit correctly is q = 1 - 0.2 = 0.8
We want the probability that the message will be wrong when decoded.
This can be written as:
![P(X\geq3) =P(X=3)+P(X=4)+P(X=5)\\P(X\geq3) =\frac{5!}{3!2!}(0.2)^3(0.8)^{2}+\frac{5!}{4!1!}(0.2)^4(0.8)^{1}+\frac{5!}{5!}(0.2)^5(0.8)^0\\P(X\geq3) =0.05792](https://tex.z-dn.net/?f=P%28X%5Cgeq3%29%20%3DP%28X%3D3%29%2BP%28X%3D4%29%2BP%28X%3D5%29%5C%5CP%28X%5Cgeq3%29%20%3D%5Cfrac%7B5%21%7D%7B3%212%21%7D%280.2%29%5E3%280.8%29%5E%7B2%7D%2B%5Cfrac%7B5%21%7D%7B4%211%21%7D%280.2%29%5E4%280.8%29%5E%7B1%7D%2B%5Cfrac%7B5%21%7D%7B5%21%7D%280.2%29%5E5%280.8%29%5E0%5C%5CP%28X%5Cgeq3%29%20%3D0.05792)
Hence, the probability that the message will be wrong when decoded is 0.05792
Answer: ![\$10,\ \$5](https://tex.z-dn.net/?f=%5C%2410%2C%5C%20%5C%245)
Step-by-step explanation:
(a) Given
Sam charge $5 for each dog for a thirty minute walk
For an hour which is double the thirty minutes, it must be double of the same charge.
![\Rightarrow 2\times 5=\$10](https://tex.z-dn.net/?f=%5CRightarrow%202%5Ctimes%205%3D%5C%2410)
(b)Given
With $20, Christie sells 100 cups of lemonade with a quarter per cup charge
For 100 cup, she generate a revenue of
![\Rightarrow \dfrac{1}{4}\times 100\\\\\Rightarrow \$25](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B1%7D%7B4%7D%5Ctimes%20100%5C%5C%5C%5C%5CRightarrow%20%5C%2425)
So, she earns
that is , her profit is ![\$5](https://tex.z-dn.net/?f=%5C%245)