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. front door of the house back door of the house blue sticker 4 3 green sticker 2 3 what is the probability that a randomly selected key is labeled with a blue sticker or opens the front door of the house? simplify 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. front door of the house back door of the house blue sticker 4 3 green sticker 2 3 what is the probability that a randomly selected key is labeled with a blue sticker or opens the front door of the house? simplify any fractions.

Answer

Explanation:

Step1: Calculate total number of keys

The total number of keys is $4 + 3+2 + 3=12$.

Step2: Calculate number of blue - stickered keys

The number of keys with blue stickers is $4 + 3=7$.

Step3: Calculate number of keys that open front - door

The number of keys that open the front - door is $4+2 = 6$.

Step4: Calculate number of keys that are blue - stickered and open front - door

The number of keys that are blue - stickered and open the front - door is 4.

Step5: Use the addition rule of probability

The formula for $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $A$ is the event of a key having a blue sticker and $B$ is the event of a key opening the front - door. $P(A)=\frac{7}{12}$, $P(B)=\frac{6}{12}$, $P(A\cap B)=\frac{4}{12}$. $P(A\cup B)=\frac{7 + 6-4}{12}=\frac{9}{12}=\frac{3}{4}$.

Answer:

$\frac{3}{4}$