SOLUTION: On a certain day, a cheese packaging facility packaged 550 units of mozzarella cheese. Some these packages had major flaws, some had minor flaws, and some had both major and flaws.

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Question 1082211: On a certain day, a cheese packaging facility packaged 550 units of mozzarella cheese. Some these packages had major flaws, some had minor flaws, and some had both major and flaws. The following table presents the results.
Minor Flaw No Minor Flaw
24 38
Major Flaw
No major Flaw 71 417
Find the probability that randomly chosen cheese package has a flaw (major or minor).
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Minor Flaw No Minor Flaw Total
Major Flaw 24 38 62
No Major flaw 71 417 488
Total 95 455 550

There are a total of 95 that have a minor flaw (add up the values in the "minor flaw" column 24+71 = 95). See bottom of column 1.

There are a total of 62 that have a major flaw (add up the values in the "major flaw" row 24+38 = 62). See end of row 1.

There are 95+62 = 157 that have either a minor or major flaw. We can add like this because of the mutually exclusive events. The flaw is major or it is minor. The flaw can't be both. There is no overlap.

This is out of 550 packs total.

P(major or minor flaw) = probability of getting a pack with either a major or minor flaw
P(major or minor flaw) = (# with major or minor flaws)/(# total)
P(major or minor flaw) = 157/550
P(major or minor flaw) = 0.285455 (approximate)
P(major or minor flaw) = 28.5455% (approximate)

The answer as a fraction is 157/550
The answer as a decimal is approximately 0.285455
The answer as a percentage is approximately 28.5455%