If about 3000 of every recall model of a vehicle actually need rework, what is the probability that your (recalled) car will not need a rework if there are 120000 cars of that model sold, and if 1000 of them are already off the road (this is a monkey wrench!). State your assumptions
To calculate the probability that your recalled car will not need a rework, we first need to determine the total number of recalled cars that may need rework and the total number of cars that are currently on the road and not yet fixed.
Assumptions:
1. All recalled cars have an equal probability of needing rework.
2. The monkey wrench (1000 cars already off the road) does not impact the probability of a car needing rework.
Let's break down the problem step by step:
Step 1: Determine the total number of recalled cars that may need rework.
Given that there are 3000 of every recall model that actually need rework, and there are a total of 120,000 cars of that model sold, we can calculate the total number of recalled cars needing rework as follows:
Total number of recalled cars needing rework = (3000 / 120,000) * 120,000 = 3000
Step 2: Calculate the total number of cars that are currently on the road and not yet fixed.
Given that there are already 1000 cars off the road due to the monkey wrench, we can calculate the remaining number of cars on the road and not yet fixed as follows:
Total number of cars on the road and not yet fixed = 120,000 - 1000 = 119,000
Step 3: Calculate the probability that a recalled car will not need a rework.
To determine the probability that your recalled car will not need a rework, we divide the number of cars that will not need rework by the total number of recalled cars:
Probability = (Total number of cars not needing rework) / (Total number of recalled cars)
Total number of cars not needing rework = Total number of cars on the road and not yet fixed - Total number of recalled cars needing rework = 119,000 - 3000 = 116,000
Probability = 116,000 / 3000 = 0.3867 or 38.67%
Therefore, the probability that your recalled car will not need a rework is approximately 38.67%.
Please keep in mind that these calculations are based on the assumptions provided above.