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Assume that a procedure yields a binomial distribution with a trial repeated n = 9 times. Find the probability of x = 4 successes given the probability p = 0.59 of success on a single trial. (Report answer accurate to 4 decimal places.) P ( 4 ) =

Respuesta :

We have a closed formula to get the probability of having a certain number of successes over repeated trials following a binomial distribution.

The formula is

[tex]\displaystyle P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}[/tex]

Where:

  • [tex]X[/tex] is the random variable
  • [tex]n[/tex] is the number of trials
  • [tex]k[/tex] is the number of desired successes
  • [tex]p[/tex] is the probability of success

So, in your case, the probability becomes

[tex]\displaystyle P(X=4)=\binom{9}{4}0.59^4(0.41)^{5}\approx 0.1768[/tex]

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