Answer to Question #113700 in Statistics and Probability for Katenda

Question

QUESTIONS 4, 5 ARE BASED ON THE FOLLOWING INFORMATION.

A Check found that sources of fake news on Facebook are mostly GP. Suppose that 20% of profiles on Facebook are GP. Suppose further that we randomly select 20 Facebook profiles and check whether or not they are GP.

Question 4

Which one of the following statements is incorrect?

(1) The given information describes a binomial experiment with possible outcomes; GP
or not GP.
(2) The number of trials is 20
(3) The 20 trials are independent of each other
(4) The probability of success or GP is 20 trials
(5) The probability of failure or “not GP” is 0.8

Question 5

Which one of the following statements is incorrect?

(1) The probability that all 20 profiles are GP is 0
(2) The probability that no profiles are GP is 0.0115
(3) The probability that only 13 profiles are GP is 0
(4) The probability that only 12 profiles are GP is 0.0001
(5) None of the above

Answer 1

$\text{ Let X be number of profiles on Facebook are GP}\\ then\; P(x)=C_{x}^{20}(0.2)^{x}(0.8)^{20-x}, x=0,1,...,20\\ Question \;4\\ \text{ the incorrect statements is }\\ \text{(4) The probability of success or GP is 20 trials}\\ \text{because the probability of success or GP is 0.20}\\ Question \;5\\ (1)P(x=20)=C_{20}^{20}(0.2)^{20}(0.8)^{20-20}\approx 0\\ (1)P(x=0)=C_{0}^{20}(0.2)^{0}(0.8)^{20-0}=0.0115\\ (1)P(x=13)=C_{13}^{20}(0.2)^{13}(0.8)^{20-13}\\ =0.00001\approx 0.0000 \\ (1)P(x=12)=C_{12}^{20}(0.2)^{12}(0.8)^{20-12}\\ =0.00008\approx 0.0001\\ \text{ the incorrect statements is }\\ \text{(5) None of the above}$