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On a given day the chance of rain is 0.4. When it rains, the chance a match is called off is 0.5. What is the chance of both?
AIt is 0.9
BIt is 0.5
CIt is 0.1
DIt is 0.2
Answer & Solution
Correct answer: D. It is 0.2
1. Two events happen one after the other, so a tree diagram fits the situation.
2. The first branch of the tree is rain, with a probability of 0.4.
3. The branch that follows it is the match being called off, with a probability of 0.5.
4. The probability of an outcome is found by multiplying along the path to that outcome.
5. So multiply 0.4 by 0.5.
6. That gives 0.2, which is the chance of rain and a cancelled match together.
7. Answering 0.9 adds the two probabilities, which would count a path that does not exist.
8. Answering 0.5 uses the second branch alone and ignores the chance of rain.
_Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 10: Probability_
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