Question

The probability that project A will succeed is 60%, that project B will succeed is 25%, and that project C will succeed is 80%. Find the probability that all 3 projects fail.Group of answer choices4.8%13.5%88%6%

Answer 1

Solution:

Given:

Probability of success for the three projects;

$\begin{gathered} P(A)=60\text{ \%}=\frac{60}{100}=0.6 \\ P(B)=25\text{ \%}=\frac{25}{100}=0.25 \\ P(C)=80\text{ \%}=\frac{80}{100}=0.8 \end{gathered}$

To get the probability of failure, use the formula;

$\begin{gathered} P=1-Q \\ where: \\ P\text{ is the probability of success} \\ Q\text{ is the probability of failure} \end{gathered}$

Hence,

$\begin{gathered} Q(A)=1-0.6=0.4 \\ Q(B)=1-0.25=0.75 \\ Q(C)=1-0.8=0.2 \end{gathered}$

Thus, the probability that all 3 projects fail is;

$\begin{gathered} Q(ABC)=0.4\times0.75\times0.2 \\ Q(ABC)=0.06 \\ \\ As\text{ a percentage;} \\ Q(ABC)=0.06\times100 \\ Q(ABC)=6\text{ \%} \end{gathered}$

Therefore, the probability that all 3 projects fail is 6%