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. what is the probability that a randomly selected competitor was female or did not react in 0.3 to 0.7 seconds? simplify any fractions.

Explanation:

Step1: Calculate total number of competitors

Add all the values in the table: \(5 + 6+5 + 4=20\)

Step2: Calculate number of female competitors or those not in \(0.3 - 0.7\) seconds

Number of female competitors: \(5 + 4 = 9\). Number of competitors not in \(0.3 - 0.7\) seconds (i.e., in less than \(0.3\) seconds): \(5+5 = 10\). But we double - counted the female competitors in less than \(0.3\) seconds (which is \(5\)). So using the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\), we have \(9 + 10-5=14\)

Step3: Calculate the probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{14}{20}=\frac{7}{10}\)

Answer:

\(\frac{7}{10}\)