While visiting her grandparents, Lucy found a box with a surprising number of spare keys. Lucy figured that the color of the sticker on each key must indicate what the key was for. When Lucy tested the keys, she was surprised to find that this was not the case.Blue sticker Green stickerFront door of the house 5 2Back door of the house 5 3Car 2 8What is the probability that a randomly selected key opens the car given that the key is labeled with a blue sticker?Simplify any fractions.
Question
While visiting her grandparents, Lucy found a box with a surprising number of spare keys. Lucy figured that the color of the sticker on each key must indicate what the key was for. When Lucy tested the keys, she was surprised to find that this was not the case.Blue sticker Green stickerFront door of the house 5 2Back door of the house 5 3Car 2 8What is the probability that a randomly selected key opens the car given that the key is labeled with a blue sticker?Simplify any fractions.
Solution
To solve this problem, we need to use the concept of conditional probability.
First, let's find out how many keys have a blue sticker. According to the table, there are 5 keys for the front door, 5 keys for the back door, and 2 keys for the car, all with blue stickers. So, the total number of blue sticker keys is 5 + 5 + 2 = 12.
Next, we need to find out how many of these blue sticker keys are for the car. According to the table, there are 2 car keys with blue stickers.
The probability that a randomly selected key opens the car given that the key is labeled with a blue sticker is therefore 2 (the number of car keys with blue stickers) divided by 12 (the total number of keys with blue stickers).
So, the probability is 2/12, which simplifies to 1/6.
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