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With global pandemic of COVID-19, media is all the time buzzing the rumors. A layman has...

With global pandemic of COVID-19, media is all the time buzzing the rumors. A layman has 65% chance of believing such rumors. Find the probability that at least 10 persons do not believe such rumors before the 3rd person who believes it.

math   Statistics-And-Probability   
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Answer #1

Ans:

Use Negative binomial distribution with r=3 and p=0.65

where x = r, r + 1, r + 2, ...

x P(x)
3 0.2746
4 0.2884
5 0.2018
6 0.1177
7 0.0618
8 0.0303
9 0.0141
10 0.0064
11 0.0028
12 0.0012
13 0.0005
14 0.0002
15 0.0001
16 0.0000
17 0.0000
18 0.0000
19 0.0000
20 0.0000

P(x>=13)=1-P(x<=12)

=1-0.9992=0.0008

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