Answer:
Option A) 0.02
Step-by-step explanation:
The probability p that one of the questions is correct is
[tex]P = \frac{1}{4}[/tex]
The number of questions that will answer (number of trials) is [tex]n = 3[/tex].
We want to find out the probability that [tex]x = 3[/tex] three questions will be answered correctly.
To calculate this probability we use the binomial formula:
[tex]P(x) = \frac{n!}{x!(n-x)!} p^x(1-p)^{n-x}[/tex]
Where
[tex]x=3\\n=3\\p=0.25[/tex]
Then:
[tex]P(x=3) = \frac{3!}{3!(3-3)!} 0.25^3(1-0.25)^{3-3}[/tex]
[tex]P(3) =0.25^3[/tex]
[tex]P(3) = 0.0156[/tex]
P(3) = 0.0156≈0.02
