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What is the probability of #X= 6# successes, using the binomial formula?

Let #n=13, p = .43#.

Answer 1

#P(X=6) ~~ 0.2121#, or approximately #21.21%#.

The binomial formula states that the probability of getting exactly #x# successes out of #n# trials (where each independent trial has success probability #p#) is

#P(X=x)=((n),(x))p^x(1-p)^(n-x)," "x=0,1,2,...,n#

where

To obtain an answer, we simply plug in the given values of #n#, #p#, and #x#:

#P(X=6)=((13),(6))(.43)^6(1-.43)^(13-6)#

#color(white)(P(X=6))=(13!)/(6!(13-6)!)(.43)^6(.57)^7#

#color(white)(P(X=6)) ~~ (1716)(0.006321)(0.015949) #

#color(white)(P(X=6)) ~~ 0.2121 #

So, out of 13 trials, the probability of obtaining exactly 6 successes is

#P(X=6) ~~ 0.2121# #color(white)(P(X=6)) = 21.21%#.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.