at a science museum, visitors can compete to see who has a faster reaction time. competitors watch a red…

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.\nmale female\nless than 0.3 seconds 5 5\n0.3 to 0.7 seconds 6 4\nwhat is the probability that a randomly selected competitor was female or did not react in 0.3 to 0.7 seconds?\nsimplify any fractions.

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.\nmale female\nless than 0.3 seconds 5 5\n0.3 to 0.7 seconds 6 4\nwhat is the probability that a randomly selected competitor was female or did not react in 0.3 to 0.7 seconds?\nsimplify any fractions.

Answer

Explanation:

Step1: Calculate total number of competitors

The total number of competitors is the sum of all values in the table. So, $(5 + 5+6 + 4)=20$.

Step2: Calculate number of females

The number of female competitors is $5 + 4=9$.

Step3: Calculate number of competitors not in 0.3 - 0.7 seconds range

The number of competitors not in the 0.3 - 0.7 seconds range is $5+5 = 10$.

Step4: Calculate number of females not in 0.3 - 0.7 seconds range

The number of females not in the 0.3 - 0.7 seconds range is 5.

Step5: Use the addition - rule for probability

The formula for $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let $A$ be the event of being female and $B$ be the event of not reacting in 0.3 - 0.7 seconds. $P(A)=\frac{9}{20}$, $P(B)=\frac{10}{20}$, and $P(A\cap B)=\frac{5}{20}$. $P(A\cup B)=\frac{9 + 10-5}{20}=\frac{14}{20}=\frac{7}{10}$.

Answer:

$\frac{7}{10}$