Question

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

Answer 1

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)

• x = 3
• n = 6
• p = 0.5

#1: Formula:

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

#2: Faster method

binompdf(6, 0.5, 3) = 0.3125