Question

Find the probability of exactly three successes in six trails of a binomial experiment in which the probability of success is 50%
Round to the nearest tenth of a percent.

Answer 1

Answer:

31.30%

Step-by-step explanation:

The probability distribution of a binomial distribution is given by :

P(x = k) = n! /k!(n - k)! P^x(1 - P)^(n - k)

In our case :

n = 6

P = 50/100 = 0.5

Now we want the probability that:

x = 3

This is because the question states that we want the probability that the number of successes are exactly 3.

We do the substitution in the probability distribution function as follows :

P(x = 3) = 6!/3!(6 - 3)! × 0.5³ × (1 - 0.5)³

= 0.3125

= 31.25%

= 31.30%

Answer 2

Answer:

Step-by-step explanation:

Formula used:

The probability mass function of binomial distribution is

$P[X=x]=nC_x\:p^x\:q^{n-x}$

x=0, 1, 2...........n

n - number of trials

p - probability of success

q - probability of failure

X- number of success

Given:

$n=6$

$p=\frac{50}{100}=\frac{1}{2}$ 

$q=\frac{1}{2}$ 

$P[X=3]=6C_3\:(\frac{1}{2})^3\:(\frac{1}{2})^{6-3}$

$P[X=3]=6C_3\:(\frac{1}{2})^3\:(\frac{1}{2})^{3}$

$P[X=3]=\frac{6*5*4}{1*2*3}\:(\frac{1}{2})^6$

$P[X=3]=20\:(\frac{1}{2^6})$

$P[X=3]=\frac{20}{64}$

$P[X=3]=\frac{5}{16}$

$P[X=3]=0.312$

P[X=3]=30%