Question

If the probability is 0.55 that a person will believe in a piece of fake news, find the probability that the 10th person to hear the fake news will be the 7th one to believe it. What is the probability that the first two to hear the fake news do not believe it?*

Answer 1

Probability that the 10th person to hear the news is the 7th one to believe it = 0.117

Probability that the first two to hear the fake news do not believe it = 0.2025

Step-by-step explanation:

Given: Probability is 0.55 that a person will believe in a piece of fake news.

Find: The probability that the 10th person to hear the fake news will be the 7th one to believe it. What is the probability that the first two to hear the fake news do not believe it?

Solution:  

Let A be an event where the person believes a fake news.

Then we have P (A) = 0.55

So P(A`) = 1-0.55 = 0.45

The 10th person to hear the fake news also believes it and he is the 7th (meaning out of 9 persons before him, 6 must also believe the fake news)

So the required probability = 9C6 (0.55)^6 (0.45)^3 * 0.55

= 9! / 3!6! * 0.55^7 * 0.45^3

= 9*8*7 / 3*2 (0.55^7 * 0.45^3)

= 0.117

Probability that the first two persons to hear the fake news does not believe it

= 0.45 * 0.45

= 0.2025

Answer 2

The probability that the 10th person to hear the news is the 7th one to believe it is 0.117

Probability that first two to hear the fake news does not believe it is 0.2025

Step-by-step explanation:

Let A be an even such that

A: Person believing in fake news

Then, given that

$P(A) = 0.55$

$P(\bar A)=1-0.55=0.45$

The 10th person to hear the fake news also believes it and he is the 7th

i.e. out of 9 persons before him, 6 must believe the fake news

Thus, the required probability

$=^9C_6(0.55)^6(0.45)^3\times 0.55$

$=\frac{9!}{3!6!}\times 0.55^7\times 0.45^3$

$=\frac{9\times 8\times 7}{3\times 2}\times 0.55^7\times 0.45^3$

$=0.117$

Probability that the first two persons to hear the fake news does not believe it

$=0.45\times 0.45$

$=0.2025$

Hope this answer is helpful.

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