Question 1179637: A company owns a fleet of 20 cars, each having either manual or automatic transmission and either 2 or 4 door models, and of these, 12 have automatic transmission. There are only 4 car with manual transmission . if a car is picked at radon from the fleet, calculate the probability that it is :
a)automatic
b)automatic or 2-door
c)automatic and 2-door
d)4-door
e)automatic given that it is a 4-door car
f) 4-door car given that it is automatic
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this probability problem step-by-step.
**1. Define the Variables**
* Total Cars: 20
* Automatic Transmission (A): 12 cars
* Manual Transmission (M): 4 cars
* 2-Door (2D)
* 4-Door (4D)
**2. Deduce Information**
* Since there are 20 total cars, 12 automatic, and 4 manual, then 20-12-4 = 4 cars are unaccounted for. This indicates an error in the problem description. It should be 8 manual cars. However, we will solve the problem as given.
**3. Calculate Probabilities**
* **a) Automatic (A)**
* P(A) = (Number of automatic cars) / (Total cars)
* P(A) = 12 / 20 = 3 / 5 = 0.6
* **b) Automatic or 2-Door (A or 2D)**
* We need more information to calculate this accurately. We need to know how many 2-door cars there are, and how many of those are automatic. However, we can use the general formula:
* P(A or 2D) = P(A) + P(2D) - P(A and 2D)
* Without knowing the distribution of 2-door cars, we cannot provide an exact answer.
* **c) Automatic and 2-Door (A and 2D)**
* We need the number of cars that are both automatic and 2-door. Without that information, we cannot calculate the probability.
* **d) 4-Door (4D)**
* We need the number of 4-door cars to calculate this. Without that information, we cannot calculate the probability.
* **e) Automatic given that it is a 4-Door car (A|4D)**
* P(A|4D) = P(A and 4D) / P(4D)
* We need the number of automatic 4-door cars and the total number of 4-door cars. Without that information, we cannot calculate the probability.
* **f) 4-Door car given that it is automatic (4D|A)**
* P(4D|A) = P(4D and A) / P(A)
* We need the number of automatic 4-door cars. We know P(A) = 12/20.
* Without the number of automatic 4-door cars, we cannot calculate the probability.
**To solve parts (b), (c), (d), (e), and (f), we need additional information about the distribution of 2-door and 4-door cars within the fleet.**
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