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 4 4\n0.3 to 0.7 seconds 5 6\nwhat is the probability that a randomly selected competitor reacted in less than 0.3 seconds given that the competitor was male?\nsimplify any fractions.
Answer
Answer:
$\frac{4}{9}$
Explanation:
Step1: Find total male competitors
$4 + 5=9$
Step2: Find male competitors with reaction time < 0.3 s
4
Step3: Calculate conditional probability
The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if $A$ is the event of reacting in less than 0.3 seconds and $B$ is the event of being male, the probability is $\frac{\text{Number of male and < 0.3 s}}{\text{Number of male}}=\frac{4}{9}$