# Probability question (5000 tires, 200 defective, 4800 good)

Today Nicole from Lenmore, CA, asked this question:

There are 5000 tires made including 200 that are defective if 4 tires are randomly selected, what is the probability that they are good?

Asked to use the method of redundancy but I'm having a hard time understanding how to write the equation and solve the problem.

The Wheeling Tire Company produced a batch of 5000 tires that includes exactly 200 that are defective.

a) If 4 tires are randomly selected for installation on a car, what is the probability that they are all good?

b) If 100 tires are randomly selected for shipment to an outlet, what is the probability that they are all good? Should the outlet plan to deal with defective tires returned by their customers?

Hi Nicole, thanks for asking. Here's how I would do this problem.

T= total number of tires
D = total number of defective tires
G = total number of good tires

2. Write an equation that represents the relationship between these variables

T = D + G

(Total number of tires) = (number of defective tires) + (number of good tires)

From this equation we can conclude that the probability of selecting a good tire is going to be:

P = G/T

3. Find the probability of selecting one good tire from the total number of tires

For this problem it helps to remember you are working with four tires, so let's label them individually as t1, t2, y3, and t4. In order to calculate the probability that ALL tires are good, you have to first calculate the individual probabilities then multiply them together.

Remember to think practically here. Every time we select a tire for use, we must subtract one from the total

P(t1, good) = 4800/5000

P(t2, good) = 4799/4999

P(t3, good) = 4798/4998

P(t4, good) = 4797/4997

Let's go ahead and keep them in fraction form to avoid miscalculating a decimal.

4. Multiply the individual probabilities to find the combined probability.

P(t1234, good) = (4800/5000)x(4799/4999)x(4798/4998)x(4797/4997) = 0.849

Make sure to go back and check that all your numbers are correct.

I hope this helps! Honestly part B) is above my level, but I found the answer here:

http://fredmath.net/Statistics/lecture2/sec2.2/sec-2.2_sol.pdf

It looks like for part B you have to use the 5% guideline, which I'm hoping your teacher can explain better than I can.

Cheers,
John W.

My questions to other tutors:

1) How would you go about solving this problem?

2) Do you agree with the methods I used?

3) Any suggestions for improvement? I am fairly new to tutoring, seeking to refine my skills in any way that I can. I grow every day through constructive feedback \$40p/h

John W.

Private tutor - proficient in Math, Language Arts, and Music

50+ hours
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