Answer:
P=65%
Step-by-step explanation:
Binomial Distribution
The probability will be calculated by using the Binomial Distribution with n independent events each with a probability of success equal to p with k successes.
The PMF (Probability Mass Function) is
[tex]\displaystyle F(k,n,p)=\binom{n}{k}p^kq^{n-k}[/tex]
Where
[tex]q = 1-p[/tex]
We have n=5trials with k=2, 3, or 4 successes. Each individual experience has [tex]p = 0.4 , q = 0.6[/tex]
First, we compute for k=2
[tex]\displaystyle F(2,5,0.4)=\binom{5}{2}0.4^20.6^{3}=0.3456[/tex]
Now for k=3
[tex]\displaystyle F(3,5,0.4)=\binom{5}{3}0.4^30.6^{2}=0.2304[/tex]
Finally for k=4
[tex]\displaystyle F(4,5,0.4)=\binom{5}{4}0.4^40.6^{1}=0.0768[/tex]
The required probability is
[tex]P=0.3456+0.2304+0.0768=0.6528[/tex]
P=65%
