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.Organic Non-organicApples 5 6Peaches 2 5What is the probability that a randomly selected participant tasted peaches or preferred organic?Simplify any fractions.
Question
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.Organic Non-organicApples 5 6Peaches 2 5What is the probability that a randomly selected participant tasted peaches or preferred organic?Simplify any fractions.
Solution
To solve this problem, we first need to understand the total number of participants and the number of participants who tasted peaches or preferred organic.
Step 1: Calculate the total number of participants The total number of participants is the sum of all the participants who tasted each type of fruit, whether organic or non-organic. So, we add all the numbers given:
Total participants = 5 (organic apples) + 6 (non-organic apples) + 2 (organic peaches) + 5 (non-organic peaches) = 18 participants
Step 2: Calculate the number of participants who tasted peaches or preferred organic This is the sum of the participants who tasted organic peaches, non-organic peaches, and organic apples.
Participants who tasted peaches or preferred organic = 2 (organic peaches) + 5 (non-organic peaches) + 5 (organic apples) = 12 participants
Step 3: Calculate the probability The probability that a randomly selected participant tasted peaches or preferred organic is the number of participants who tasted peaches or preferred organic divided by the total number of participants.
Probability = Number of favorable outcomes / Total number of outcomes
So, the probability = 12 (participants who tasted peaches or preferred organic) / 18 (total participants) = 2/3
Therefore, the probability that a randomly selected participant tasted peaches or preferred organic is 2/3.
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