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

while visiting his grandparents, jamie found a box with a surprising number of spare keys. jamie figured that the color of the sticker on each key must indicate what the key was for. when jamie tested the keys, he was surprised to find that this was not the case.\n\n| |front door of the house|back door of the house|\n|--|--|--|\n|blue sticker|4|3|\n|green sticker|2|3|\n\nwhat is the probability that a randomly selected key is labeled with a blue sticker or opens the front door of the house?\n\nsimplify any fractions.

while visiting his grandparents, jamie found a box with a surprising number of spare keys. jamie figured that the color of the sticker on each key must indicate what the key was for. when jamie tested the keys, he was surprised to find that this was not the case.\n\n| |front door of the house|back door of the house|\n|--|--|--|\n|blue sticker|4|3|\n|green sticker|2|3|\n\nwhat is the probability that a randomly selected key is labeled with a blue sticker or opens the front door of the house?\n\nsimplify any fractions.

Answer

Answer:

$\frac{3}{4}$

Explanation:

Step1: Calculate total number of keys

$4 + 3+2 + 3=12$

Step2: Calculate number of keys with blue - sticker or open front - door

Number of blue - sticker keys: $4 + 3=7$. Number of keys opening front - door: $4+2 = 6$. Keys that are blue - sticker and open front - door: $4$. Using the formula $n(A\cup B)=n(A)+n(B)-n(A\cap B)$, we have $7 + 6-4 = 9$.

Step3: Calculate the probability

Probability $P=\frac{9}{12}=\frac{3}{4}$