while visiting his grandparents, colton found a box with a surprising number of spare keys. colton figured…

while visiting his grandparents, colton found a box with a surprising number of spare keys. colton figured that the color of the sticker on each key must indicate what the key was for. when colton tested the keys, he was surprised to find that this was not the case. what is the probability that a randomly selected key opens the back door of the house given that the key is labeled with a green sticker? simplify any fractions.

while visiting his grandparents, colton found a box with a surprising number of spare keys. colton figured that the color of the sticker on each key must indicate what the key was for. when colton tested the keys, he was surprised to find that this was not the case. what is the probability that a randomly selected key opens the back door of the house given that the key is labeled with a green sticker? simplify any fractions.

Answer

Explanation:

Step1: Find total green - stickered keys

The total number of keys with green stickers is the sum of green - stickered keys for front door and back door. So, $5 + 5=10$.

Step2: Find green - stickered keys for back door

The number of green - stickered keys for the back door is 5.

Step3: Calculate the conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if $A$ is the event that the key opens the back door and $B$ is the event that the key has a green sticker, then the probability that a key opens the back door given it has a green sticker is $\frac{\text{Number of green - stickered keys for back door}}{\text{Total number of green - stickered keys}}=\frac{5}{10}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$