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Ostrovityanka [42]

3 years ago

9

A student wants to conduct an experiment to see how quickly information can travel. On Day 1 of the experiment, the student tell

s three friends a personal fact. On Day 2, those three friends share the fact with three new people each. Assuming this pattern continues, how many people will hear the fact on Day 7 of the experiment?

1 answer:

Aliun [14]3 years ago

7 0

3 people know a fact in 1st day.
In 2nd day they share it with 3 people each=3×3
Now 3×3 people shares it with 3 people each. and so on...
So,
3+3²+3³+3⁴+3^5+3^6+3^7
=3279 no of people altogether , will hear from 1st day to 7th day...
On the day 7,no of people who will hear the fact=3^7=2187

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We use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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And p is the probability of X happening.

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This means that $p = 0.23$

a) In a sample of six British citizens, what is the probability that two have ever boycotted goods for ethical reasons?

This is P(X = 2) when n = 6. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{6,2}.(0.23)^{2}.(0.77)^{4} = 0.2789$

27.89% probability that two have ever boycotted goods for ethical reasons

b) In a sample of six British citizens, what is the probability that at least two respondents have boycotted goods for ethical reasons?

Either less than two have, or at least two. The sum of the probabilities of these events is decimal 1. So

$P(X < 2) + P(X \geq 2) = 1$

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1)$

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$P(X = 1) = C_{6,1}.(0.23)^{1}.(0.77)^{5} = 0.3735$

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$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.5819 = 0.4181$

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