Answer :
Explanation
To solve this problem, we will use the formula for the probability of the Binomial distribution:
[tex]b(x;n,p)=\frac{n!}{(n-x)!\cdot x!}\cdot p^x\cdot(1-p)^{n-x}.[/tex]Where:
• b(x; n, p) = the binomial probability for x,
,• x = the total number of successes,
,• n = the number of trials,
,• p = the probability of success on an individual trial.
From the statement, we know that:
• x = 5,
,• n = 10,
,• p = 0.2.
Replacing these data in the formula above, we get:
[tex]b(5;10,0.2)=\frac{10!}{(10-5)!\cdot5!}\cdot0.2^5\cdot(1-0.2)^{10-5}\cong0.026.[/tex]Answer0.026