If the probability that Joe will buy a pizza is 0.5 and the probability that Elaine will buy a pizza

Keenan Santos

Keenan Santos

Answered question

2022-07-09

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.

Answer & Explanation

lywiau63

lywiau63

Beginner2022-07-10Added 13 answers

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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