Tammy and Mom at the supermarket
"There are a total of 2 different toys in these mystery boxes in the local supermarket. Each mystery box contains a different type of toy!" Tammy said gleefully.
"Not so fast." Tammy's mother said. "I want to know the average number of boxes I will need to buy to get you both toys.
"Well, the chances of getting a specific type of toy is 50%, and the chances of me getting both toys is independent from each other, so the chances of me getting both toys is 50% of 50%, which is 25%! So on average, 4 boxes will be enough." Tammy said.
"Goodness, looks like I will need to buy you 4 boxes to get what you want." Tammy's mother said sadly.
Is Tammy's reasoning correct?
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1 solution
The problem with Tammy's reasoning is that the first box he chooses will guarantee him with 1 of the 2 type of toys, so all he needs to do is get the other type of toy, which is indeed 50%. So the number of boxes Tammy should get is 1 + 100%/50% = 1 + 2 = 3, which is not 4.