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

Question

asked Aug 14, 2022 203k views

2 Answers

Reini · Answer 1 · 2022-08-18T11:56:42+0000

Answer: 31.25%

Two ways to solve this problem:

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

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

#1: Formula:

$P(X=3)=_(6)C_(3)*0.5^(3) *(1-0.5)^(6-3)=(6!)/(3!(6-3)!) *0.5^(3) *0.5^(3)\\=(6!)/(3!*3!) *0.5^(3) *0.5^(3)=20*0.125*0.125=0.3125$

#2: Faster method

binompdf(6, 0.5, 3) = 0.3125