Answer to Question #190470 in Statistics and Probability for charm

Question

Suppose that the probability is 0.8 that any person will believe a fake news about a celebrity, what is the probability that (a) the tenth person to read the news is the seventh person to believe it? (b) the fourth person to read the news if the second person to believe it?

Answer 1

We have given that,

$p = 0.8$

$q = 0.2$

a.) We have to find the probability that the tenth person to read the news is the seventh person to believe it.

Using the binomial distribution,

$P(X= 10) = ^{10}C_7(0.8)^7(0.2)^{10-7}$

$= ^{10}C_7(0.8)^7(0.2)^{3}$

b.) We have to find the probability that the fourth person to read the news is the second person to believe it.

$P(X= 4) = ^4C_2(0.8)^2(0.2)^2$