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: 31.3 is the real answer.

Explanation:

Answer 2

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)=(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