Answer:
Let P(M) and P(E) be the probability that a student takes mathematics, and the probability that a student takes English, respectively.
Thus, P(M)=10/30, P(E)=12/30, and [ P(M) and P(E)]=5/30.
If we want the probability that a student takes neither mathematics nor English, then we are looking for the set that is a compliment to [P(M) or P(E)].
That is, we want to find 1 - [P(M) or P(E)].
According to the Additive Law of Probability,
[P(M) or P(E)] = P(M) + P(E) - [P(M) and P(E)].
Thus,
[P(M) or P(E)] = 10/30 + 12/30 - 5/30
This equals 17/30.
Therefore, the compliment to [P(M) or P(E)] is
1 - 17/30 = 13/30.
There is an approximately 43% chance of choosing a student who is taking neither mathematics nor English.
Step-by-step explanation:
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