## If the probability is 0.55 that a person will believe in a fake news. find the probability that the 10th person to hear the news is the 7th

Question

If the probability is 0.55 that a person will believe in a fake news. find the probability that the 10th person to hear the news is the 7th one believe it.also find the probability that the first two to hear the fake news does not believe it.​

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5 months 2021-08-16T13:04:53+00:00 2 Answers 0 views 0

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

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

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