SOLUTION: Caroline has a 67% chance of receiving an A grade in statistics, a 51% chance of receiving an A grade in mathematics, and a 41% chance of receiving A grades in both statistics and

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Question 426914: Caroline has a 67% chance of receiving an A grade in statistics, a 51% chance of receiving an A grade in mathematics, and a 41% chance of receiving A grades in both statistics and mathematics. Find the probability that she receives an A in statistics or mathematics (or both).

Found 2 solutions by stanbon, robertb:
Answer by stanbon(75887) (Show Source):
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Caroline has a 67% chance of receiving an A grade in statistics, a 51% chance of receiving an A grade in mathematics, and a 41% chance of receiving A grades in both statistics and mathematics. Find the probability that she receives an A in statistics or mathematics (or both).
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Draw a Venn Diagram: 2 intersecting circles.
Label one stat and the other math
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Put 41 in the intersection
Put 67-41 = 26 in stat but not in the intersection.
Put 51-41 = 10 in math but not iin the intersection
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P(stat or math or both ) = 0.26+0.41+0.10 = 0.87
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Cheers,
Stan H.
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Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website!
P(A in Math OR A in Stats) = P(A in Math) + P(A in Stats) - P(A in Math OR A in Stats) = 0.51 + 0.67 - 0.41 = 0.77, the probability that she receives an A in statistics or mathematics (or both).
It's called the General Addition Rule of Probability. No need for Venn Diagrams here.