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Find the probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50%.

Sagot :

Jessmzhou4idn

Answer: 31.25%

Two ways to solve this problem:

#1: Use the formula: [tex]P(X=x)={n}Cx_{} *p^{x}*(1-p)^{n-x}[/tex]

#2 Use a graphing calculator and use the function binompdf(n, p, x)

  • x = 3
  • n = 6
  • p = 0.5

#1: Formula:

[tex]P(X=3)=_{6}C_{3}*0.5^{3} *(1-0.5)^{6-3}=\frac{6!}{3!(6-3)!} *0.5^{3} *0.5^{3}\\=\frac{6!}{3!*3!} *0.5^{3} *0.5^{3}=20*0.125*0.125=0.3125[/tex]

#2: Faster method

binompdf(6, 0.5, 3) = 0.3125

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