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Mintfu8122

28.03.2023

Mathematics

P(X > 4) = 0.8059

Step-by-step explanation:

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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this question, we have that:

n = 8, p = 0.7

We want:

P(X 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

In which

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

$P(X = 5) = C_{8,5}.(0.7)^{5}.(0.3)^{3} = 0.2541$

$P(X = 6) = C_{8,6}.(0.7)^{6}.(0.3)^{2} = 0.2965$

$P(X = 7) = C_{8,7}.(0.7)^{7}.(0.3)^{1} = 0.1977$

$P(X = 8) = C_{8,8}.(0.7)^{8}.(0.3)^{0} = 0.0576$

Then

P(X 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.2541 + 0.2965 + 0.1977 + 0.0576 = 0.8059

P(X > 4) = 0.8059

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