At a quality control checkpoint on a manufacturing assembly line, 8% of the items failed check A, 10% failed check B, and 2% failed both checks A and B.

a. If a product failed check A, what is the probability that it also failed check B? b. If a product failed check B, what is the probability that it also failed check A?
c. What is the probability that a product failed either check A or check B?
d. What is the probability that a product failed neither check A nor check B?

I am not good with probability and the percentages are really throwing me off. Any help would be great.

Prob(B given A)=Prob(A,B)/Pr(A)

= .02/.08=.25

Sure! Probability problems with percentages can often be confusing. Let's break down the information and tackle each part of the question step by step.

a. To find the probability that a product failed check B given that it failed check A, we need to use conditional probability. In this case, we know that 2% of the items failed both checks A and B, while 8% failed check A. So the probability that a product failed both checks A and B, given that it failed check A, can be calculated as (2% / 8%) * 100 = 25%.

b. Similarly, to find the probability that a product failed check A given that it failed check B, we can use the same conditional probability approach. We know that 2% of the items failed both checks A and B, while 10% failed check B. So the probability that a product failed both checks A and B, given that it failed check B, can be calculated as (2% / 10%) * 100 = 20%.

c. The probability that a product failed either check A or check B can be found by adding the probabilities of failing each check separately and then subtracting the probability of failing both checks. So the probability of failing check A or B would be 8% + 10% - 2% = 16%.

d. The probability that a product failed neither check A nor check B can be found by subtracting the probability of failing either check A or check B from 100%. So the probability of passing both check A and check B would be 100% - 16% = 84%.

I hope this helps! Let me know if you have any further questions.