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If the probability that Joe will buy a pizza is $0.5$ and the probability that Elaine will buy a pizza is $0.35$, then what is the probability that at least one of the two will buy a pizza on their next visit to the pizza place?

I know that this is a very basic problem. However, I am a little confused about the "at least" statement in the question. I would really like to understand why the correct answer is correct, so please go in depth for how you got your answer. I am thinking that you might use the addition rule for probability, but again, the "at least" confuses me.

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1 Answer

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It means you should consider the possibilities that $(a)$ only Joe buys a pizza, $(b)$ only Elaine buys a pizza, and $(c)$ both Joe and Elaine buy a pizza.

The only way the condition is not satisfied is if neither of them buys a pizza. If the two people buy pizzas independently of each other, this happens with probability

$$ (1-0.5)(1-0.35) = (0.5)(0.65) = 0.325 $$

so the probability that at least one of them buys a pizza is $1-0.325 = 0.675$.

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