What is the probability of getting 4 or more days when the surf is at least 6 feet?
Answers
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Question:-
What is the probability of getting 4 or more days when the surf is at least 6 feet?
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Solution:-
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The probability of getting 4 or more days when the surf is at least 6 feet is 0.54
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Step-by-step explanation:
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We can modelate this exercise as a binomial random variable.
The probability function of a binomial random variable is :
P(X=r)=(nCr)p^{r}(1-p)^{n-r}P(X=r)=(nCr)p r (1−p) n−r
Where P(X=r)P(X=r) is the probability of the variable X to assume the value r
nCr is the combinatorial number define as nCr=\frac{n!}{r!(n-r)!}nCr= r!(n−r)!n!
n is the number of binomial experiments that we make. In our exercise, n is the number of random days we pick of January.
And finally p is the success probability.
In our exercise, we define X : ''The number of days when the surf is at least 6 feet''.
And we are looking for P(X≥4).
P(X≥4) = P(X = 4) + P(X = 5) + P(X = 6)
P(X=4)=6C4(0.6^{4})(0.4^{2})P(X=4)=6C4(0.6 4 )(0.42)
P(X=5)=6C5(0.6^{5})(0.4^{1})P(X=5)=6C5(0.6 5 (0.41 )
P(X=6)=6C6(0.6^{6})(0.4^{0})=0.6^{6}P(X=6)=6C6(0.6 6 )(0.4 0 )=0.6 6
Finally
P(X≥4)=6C4(0.6^{4})(0.4^{2})+6C5(0.6^{5})(0.4^{1})+0.6^{6}=0.5446C4(0.6 4 )(0.4 2 )+6C5(0.6 5 )(0.4 1 )+0.6 6
=0.544
P(X≥4) = 0.544