Question

A car repair is either on time or late and either satisfactory or unsatisfactory. If a repair is made on time, then there is a probability of 0.85 that it is satisfactory. There is a probability of 0.77 that a repair will be made on time. What is the probability that a repair is made on time and is satisfactory?

Answer 1

Answer:

0.6545

Step-by-step explanation:

Let $P(T)$ be probability of being on time and $P(S)$ the probability of being satisfactory. We have conditional probability here since being satisfactory depends on being on time. Conditional probability states

$P(S|T) =\frac{P(S\cap T)}{P(T)}$

where

$P(S|T)$ is the probability of $S$ given that $T$ has occurred;

$P(S\cap T)$ is the probability of $S$ and $T$.

Rearranging, we have

$P(S\cap T)=P(S|T)\times P(T)$

$P(S\cap T)=0.85\times0.77=0.6545$