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Taking maths has probability 0.6, taking science 0.5, and taking both 0.3. Are the two events independent?
AYes, because 0.6 times 0.5 equals 0.3
BNo, because 0.6 plus 0.5 exceeds 0.3
CNo, because 0.3 is not equal to 0.11
DYes, because 0.3 is exactly half of 0.6
Answer & Solution
Correct answer: A. Yes, because 0.6 times 0.5 equals 0.3
1. Multiplying the two separate probabilities gives 0.6 times 0.5, which is 0.3.
2. The stated joint probability is 0.3 as well, so the product test holds.
3. The same conclusion follows from the conditional: 0.3 divided by 0.5 is 0.6, which equals the probability of taking maths.
4. Knowing that a student takes science therefore leaves the chance of taking maths unchanged.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.2 Independent and Mutually Exclusive Events_
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