Exercise 2.1
A certain sports car comes equipped with either an automatic or a manual transmission, and the car is available in one of four colors. Relevant probabilities for various combinations of transmission type and color are given in the accompanying table.
| White | Blue | Black | Red | ||
| Transmission Type | A | .15 | .10 | .10 | .10 |
| Transmission Type | M | .15 | .05 | .15 | .20 |
Let $A=\{\text{automatic transmission}\}$, $B=\{\text{black}\}$, and $C=\{\text{white}\}$.
- Calculate $P(A)$, $P(B)$ and $P(A\cap B)$.
- Calculate both $P(A|B)$ and $P(B|A)$, and explain in context what each of these probabilities represents.
- Calculate and interpret $P(A|C)$ and $P(A|C^c)$.
References:
Book P83, Exer 45.