Question

now, find the probability of event c. p(c) = ?/5

Explanation:

Step1: Use the law of total probability

We consider two - stage events. The probability of reaching event C can be calculated by considering two paths: through A and through B.
The probability of going through A is $P(A)=\frac{1}{4}$, and given that we are at A, the probability of reaching C is $P(C|A)=\frac{3}{5}$. The probability of going through B is $P(B)=\frac{3}{4}$, and given that we are at B, the probability of reaching C is $P(C|B)=\frac{3}{5}$.

Step2: Apply the formula for total probability

The formula for the total probability of event C is $P(C)=P(A)\times P(C|A)+P(B)\times P(C|B)$.
Substitute the values: $P(A)\times P(C|A)=\frac{1}{4}\times\frac{3}{5}=\frac{3}{20}$, and $P(B)\times P(C|B)=\frac{3}{4}\times\frac{3}{5}=\frac{9}{20}$.
Then $P(C)=\frac{3}{20}+\frac{9}{20}=\frac{3 + 9}{20}=\frac{12}{20}=\frac{3}{5}$.

Answer:

3