a food lab conducted a blind taste test to determine if organic fruits taste better than non - organic…

a food lab conducted a blind taste test to determine if organic fruits taste better than non - organic fruits. each participant ate one type of fruit.\n| |organic|non - organic|\n|--|--|--|\n|apples|4|4|\n|peaches|5|3|\n|blueberries|5|4|\nwhat is the probability that a randomly selected participant tasted peaches given that the participant preferred organic?\nsimplify any fractions.

a food lab conducted a blind taste test to determine if organic fruits taste better than non - organic fruits. each participant ate one type of fruit.\n| |organic|non - organic|\n|--|--|--|\n|apples|4|4|\n|peaches|5|3|\n|blueberries|5|4|\nwhat is the probability that a randomly selected participant tasted peaches given that the participant preferred organic?\nsimplify any fractions.

Answer

Explanation:

Step1: Calculate total number of organic - fruit tasters

Add the number of participants who tasted organic apples, peaches, and blueberries. $4 + 5+5=14$.

Step2: Calculate number of participants who tasted organic peaches

The number of participants who tasted organic peaches is 5.

Step3: Use the conditional - probability formula

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of a two - way table, if $A$ is the event of tasting peaches and $B$ is the event of preferring organic, then $P(A|B)=\frac{\text{Number of organic peaches tasters}}{\text{Total number of organic - fruit tasters}}$. So the probability is $\frac{5}{14}$.

Answer:

$\frac{5}{14}$