a birthday party caterer counted the number of juice cups on the table. the cups contained different…
a birthday party caterer counted the number of juice cups on the table. the cups contained different flavored juices and different shaped straws.\n| |heart - shaped straw|star - shaped straw|\n|--|--|--|\n|orange juice|2|4|\n|grape juice|3|6|\nwhat is the probability that a randomly selected cup contains a star - shaped straw given that the cup contains orange juice?\nsimplify any fractions.
Answer
Explanation:
Step1: Find total orange - juice cups
The number of orange - juice cups is the sum of orange - juice cups with heart - shaped straws and star - shaped straws. So, $2 + 4=6$.
Step2: Find number of orange - juice cups with star - shaped straws
The number of orange - juice cups with star - shaped straws is 4.
Step3: Calculate 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 having a star - shaped straw and $B$ is the event of having orange juice, then the probability that a cup has a star - shaped straw given it has orange juice is $\frac{\text{Number of orange - juice cups with star - shaped straws}}{\text{Total number of orange - juice cups}}=\frac{4}{6}=\frac{2}{3}$.
Answer:
$\frac{2}{3}$