Suppose a student is selected at random from 100 students, 30 are taking Mechanical Engineering, 20 are taking Electrical Engineering and 10 are taking Mechanical and Electrical Engineering. Find the probability that the student is taking Electrical Engineering or Mechanical Engineering.
Question
Suppose a student is selected at random from 100 students, 30 are taking Mechanical Engineering, 20 are taking Electrical Engineering and 10 are taking Mechanical and Electrical Engineering. Find the probability that the student is taking Electrical Engineering or Mechanical Engineering.
Solution
To solve this problem, we need to use the formula for the probability of the union of two events, which is P(A U B) = P(A) + P(B) - P(A ∩ B).
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First, we need to find the probability of a student taking Mechanical Engineering (P(ME)). This is the number of students taking Mechanical Engineering divided by the total number of students. So, P(ME) = 30/100 = 0.3.
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Next, we need to find the probability of a student taking Electrical Engineering (P(EE)). This is the number of students taking Electrical Engineering divided by the total number of students. So, P(EE) = 20/100 = 0.2.
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Then, we need to find the probability of a student taking both Mechanical and Electrical Engineering (P(ME ∩ EE)). This is the number of students taking both divided by the total number of students. So, P(ME ∩ EE) = 10/100 = 0.1.
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Now we can use the formula to find the probability of a student taking either Mechanical or Electrical Engineering. P(ME U EE) = P(ME) + P(EE) - P(ME ∩ EE) = 0.3 + 0.2 - 0.1 = 0.4.
So, the probability that the student is taking either Electrical Engineering or Mechanical Engineering is 0.4 or 40%.
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