At a science museum, visitors can compete to see who has a faster reaction time. Competitors watch a red screen, and the moment they see it turn from red to green, they push a button. The machine records their reaction times and also asks competitors to report their gender. The probability that a competitor reacted in over 0.7 seconds is 0.6, the probability that a competitor was female is 0.4, and the probability that a competitor reacted in over 0.7 seconds and was female is 0.3. What is the probability that a randomly chosen competitor reacted in over 0.7 seconds or was female? Write your answer as a whole number, decimal, or simplified fraction. ____

Question

At a science museum, visitors can compete to see who has a faster reaction time. Competitors watch a red screen, and the moment they see it turn from red to green, they push a button. The machine records their reaction times and also asks competitors to report their gender. The probability that a competitor reacted in over 0.7 seconds is 0.6, the probability that a competitor was female is 0.4, and the probability that a competitor reacted in over 0.7 seconds and was female is 0.3. What is the probability that a randomly chosen competitor reacted in over 0.7 seconds or was female? Write your answer as a whole number, decimal, or simplified fraction.   ____

Bytelearn · Accepted Answer

Denoting the events: Let's denote the events as follows:  A: The competitor reacted in over 0.7 seconds. B: The competitor was female. We are given the following probabilities:  P(A) = 0.6  P(B) = 0.4  P(A and B) = 0.3  We need to find the probability that a randomly chosen competitor reacted in over 0.7 seconds or was female, which is P(A or B).Using the Addition Rule of Probability: We can use the Addition Rule of Probability to find P(A or B). The formula is:  P(A or B) = P(A) + P(B) - P(A and B)Substituting the given values: Substituting the given values into the formula, we get:  P(A or B) = 0.6 + 0.4 - 0.3Performing the calculation: Now we perform the calculation:  P(A or B) = 1.0 - 0.3 P(A or B) = 0.7

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