Construction Probability

Explanation

Defined:

• $A =$ event construction finishes on time
• $A^c =$ event construction does not finish on time
• $B =$ event a protest occurs
• $B^c =$ event no protest occurs
• $A|B =$ event construction finishes on time given a protest
• $A|B^c =$ event construction finishes on time given no protest

The probability that construction finishes on time is the sum of the probability of a protest multiplied by the probability of finishing on time given a protest, plus the probability of no protest multiplied by the probability of finishing on time given no protest.

We know that:

Then:

Thus, the probability that the construction finishes on time is $0.52$.