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

Identify Probabilities:  To find the probability that a randomly chosen competitor reacted in over 0.7 seconds or was female, we can use the formula for the probability of the union of two events A and B, which is P(text(A ∪ B)) = P(text(A)) + P(text(B)) - P(text(A ∩ B)). Here, event A is the competitor reacting in over 0.7 seconds, and event B is the competitor being female.Apply Formula:  First, we identify the probabilities given:P(text(A)) = Probability that a competitor reacted in over 0.7 seconds = 0.6P(text(B)) = Probability that a competitor was female = 0.4P(text(A ∩ B)) = Probability that a competitor reacted in over 0.7 seconds and was female = 0.3Perform Calculation:  Now, we apply the formula to find P(text(A ∪ B)):P(text(A ∪ B)) = P(text(A)) + P(text(B)) - P(text(A ∩ B))P(text(A ∪ B)) = 0.6 + 0.4 - 0.3Final Probability:  We perform the calculation:P(text(A ∪ B)) = 0.6 + 0.4 - 0.3P(text(A ∪ B)) = 1.0 - 0.3P(text(A ∪ B)) = 0.7The probability that a randomly chosen competitor reacted in over 0.7 seconds or was female is 0.7.

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