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.

	less than 0.3 seconds	0.3 to 0.7 seconds
male	3	5
female	3	3

what is the probability that a randomly selected competitor was male or reacted in 0.3 to 0.7 seconds?
simplify any fractions.

Explanation:

Step1: Calculate total number of competitors

Total = \(3 + 5+3 + 3=14\)

Step2: Calculate number of male competitors

Number of male = \(3 + 5 = 8\)

Step3: Calculate number of competitors with reaction time \(0.3 - 0.7\) seconds

Number of \(0.3 - 0.7\) seconds = \(5+3 = 8\)

Step4: Calculate number of male competitors with reaction time \(0.3 - 0.7\) seconds

Number of male and \(0.3 - 0.7\) seconds = \(5\)

Step5: Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

\(P(\text{male or }0.3 - 0.7)=\frac{8}{14}+\frac{8}{14}-\frac{5}{14}=\frac{8 + 8-5}{14}=\frac{11}{14}\)

Answer:

\(\frac{11}{14}\)