Eva conducted a blind taste test on some of her friends in order to determine if organic fruits taste better than non-organic fruits. Each friend ate one type of fruit.The probability that a friend tasted apples is 0.48, the probability that a friend preferred non-organic is 0.8, and the probability that a friend tasted apples and preferred non-organic is 0.46.What is the probability that a randomly chosen friend tasted apples or preferred non-organic?Write your answer as a whole number, decimal, or simplified fraction.Submit
Question
Eva conducted a blind taste test on some of her friends in order to determine if organic fruits taste better than non-organic fruits. Each friend ate one type of fruit.The probability that a friend tasted apples is 0.48, the probability that a friend preferred non-organic is 0.8, and the probability that a friend tasted apples and preferred non-organic is 0.46.What is the probability that a randomly chosen friend tasted apples or preferred non-organic?Write your answer as a whole number, decimal, or simplified fraction.Submit
Solution
The probability that a randomly chosen friend tasted apples or preferred non-organic can be calculated using the formula for the probability of the union of two events: P(A or B) = P(A) + P(B) - P(A and B).
Here, event A is that a friend tasted apples and event B is that a friend preferred non-organic.
Given in the problem, P(A) = 0.48, P(B) = 0.8, and P(A and B) = 0.46.
Substituting these values into the formula gives:
P(A or B) = P(A) + P(B) - P(A and B) = 0.48 + 0.8 - 0.46 = 0.82.
So, the probability that a randomly chosen friend tasted apples or preferred non-organic is 0.82.
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