Respuesta :
The questions have 5 options, and only one of those options is correct and four of those options are wrong.
Before we answer the question, we need to calculate two probabilities:
• the probability of getting a correct answer
,• the probability of getting a wrong answer
To calculate these probabilities, we use the probability formula:
[tex]P(x)=\frac{\text{Number of favorable outcomes}}{total\text{ number of outcomes}}[/tex]For the probability of getting a correct answer the number of favorable outcomes is 1 because only one is the correct option, and the total number of outcomes is 5 because we have 5 options.
So, the probability of a correct answer is:
[tex]P(C)=\frac{1}{5}[/tex]And for the probability of a wrong answer, since 4 of the 5 options are wrong:
[tex]P(W)=\frac{4}{5}[/tex]Now, we are asked for:
[tex]P(CCW)[/tex]So we need to use the multiplication rule to find this probability:
[tex]P(CCW)=P(C)\times P(C)\times P(W)[/tex]We substitute P(C) and P(W):
[tex]P(CCW)=\frac{1}{5}\times\frac{1}{5}\times\frac{4}{5}[/tex]To make this multiplication, we multiply all the numerators and all of the denominators:
[tex]\begin{gathered} P(CCW)=\frac{1\times1\times4}{5\times5\times5} \\ \\ P(CCW)=\frac{4}{125} \end{gathered}[/tex]We can leave the answer as a fraction, or we can convert to a decimal:
[tex]P(CCW)=\frac{4}{125}=0.032[/tex]Answer:
[tex]P(CCW)=\frac{4}{125}=0.032[/tex]