a clown made purple, green, and yellow balloon animals at a party. he kept track of the requests.\n|…

a clown made purple, green, and yellow balloon animals at a party. he kept track of the requests.\n| |giraffe|dog|\n|--|--|--|\n|purple|6|10|\n|green|3|8|\n|yellow|3|9|\nwhat is the probability that a randomly selected balloon animal is purple given that the balloon animal is shaped like a dog?\nsimplify any fractions.

a clown made purple, green, and yellow balloon animals at a party. he kept track of the requests.\n| |giraffe|dog|\n|--|--|--|\n|purple|6|10|\n|green|3|8|\n|yellow|3|9|\nwhat is the probability that a randomly selected balloon animal is purple given that the balloon animal is shaped like a dog?\nsimplify any fractions.

Answer

Explanation:

Step1: Find total number of dog - shaped balloon animals

Add the number of purple, green and yellow dog - shaped balloon animals. $10 + 8+9=27$

Step2: Find number of purple dog - shaped balloon animals

The number of purple dog - shaped balloon animals is 10.

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 of the balloon animal being purple and $B$ is the event of the balloon animal being shaped like a dog, the probability is $\frac{\text{Number of purple dog - shaped balloon animals}}{\text{Total number of dog - shaped balloon animals}}=\frac{10}{27}$

Answer:

$\frac{10}{27}$