Answer:
[tex]Pr = 0.140625[/tex]
Step-by-step explanation:
Given
[tex]n = 5[/tex] --- questions
[tex]options = 4[/tex] ---- a, b, c or d
Required
The probability that 1st correct question is the 3rd
The probability of selecting the right answer is:
[tex]p = \frac{1}{options}[/tex]
[tex]p = \frac{1}{4}[/tex]
[tex]p = 0.25[/tex]
Using complements, we have:
[tex]q = 1-p[/tex]
[tex]q = 1-0.25[/tex]
[tex]q = 0.75[/tex] --- probability of selecting the wrong answer
The required probability is represented as:
Pr = First is wrong * Second is wrong * Third is correct
[tex]Pr = q * q * p[/tex]
This gives
[tex]Pr = 0.75 * 0.75 * 0.25[/tex]
[tex]Pr = 0.140625[/tex]
