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Part 1
In a class of 146 students, 94 are taking math (M), 76 are taking science (S), and 53 are taking both math and science. One student is picked at random. Find the probability.
P(taking math or science or both)
To find the probability of a student taking math or science or both, we need to add the probabilities of each event individually and then subtract the probability of the student taking both math and science to avoid double counting.
Let's denote:
P(M) = probability of taking math
P(S) = probability of taking science
P(M ∩ S) = probability of taking both math and science
We are given:
total students = 146
students taking math (M) = 94
students taking science (S) = 76
students taking both math and science = 53
Now, we can find the probabilities:
P(M) = 94/146
P(S) = 76/146
P(M ∩ S) = 53/146
Next, we can plug these values into the formula for the probability of taking math or science or both:
P(M or S) = P(M) + P(S) - P(M ∩ S)
P(M or S) = 94/146 + 76/146 - 53/146
P(M or S) = 94/146 + 76/146 - 53/146
P(M or S) = 117/146
Therefore, the probability of a student taking math or science or both is 117/146.