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Sagot :
Answer:
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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this question, we have that:
[tex]n = 8, p = 0.7[/tex]
We want:
[tex]P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{8,5}.(0.7)^{5}.(0.3)^{3} = 0.2541[/tex]
[tex]P(X = 6) = C_{8,6}.(0.7)^{6}.(0.3)^{2} = 0.2965[/tex]
[tex]P(X = 7) = C_{8,7}.(0.7)^{7}.(0.3)^{1} = 0.1977[/tex]
[tex]P(X = 8) = C_{8,8}.(0.7)^{8}.(0.3)^{0} = 0.0576[/tex]
Then
[tex]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[/tex]
So
P(X > 4) = 0.8059
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