In a class, $40$ students take chemistry only, $30$ take physics only, $20$ take both chemistr

Question

In a class, $40$ students take chemistry only, $30$ take physics only, $20$ take both chemistry and physics, and $60$ take neither. Find the probability that a student takes physics given that the student takes chemistry. Find the probability that a student takes physics given that the student does not take chemistry. State whether the events “taking chemistry” and “taking physics” are mutually exclusive, independent, or neither. Justify your answer. [6]

Accepted Answer

$P(P\mid C')=\frac{30}{30+60}=\frac13$. Since these are equal, taking chemistry and taking physics are independent; they are not mutually exclusive because 20 students take both.

Calculate conditional set probabilities and test independence.

Calculate conditional set probabilities and test independence.

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