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.Male FemaleLess than 0.3 seconds 3 50.3 to 0.7 seconds 5 2What is the probability that a randomly selected competitor reacted in less than 0.3 seconds and was female?Simplify any fractions.
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.Male FemaleLess than 0.3 seconds 3 50.3 to 0.7 seconds 5 2What is the probability that a randomly selected competitor reacted in less than 0.3 seconds and was female?Simplify any fractions.
Solution
To find the probability that a randomly selected competitor reacted in less than 0.3 seconds and was female, we first need to find the total number of competitors.
From the data, we can see that there are:
- 3 males who reacted in less than 0.3 seconds
- 5 males who reacted in 0.3 to 0.7 seconds
- 5 females who reacted in less than 0.3 seconds
- 2 females who reacted in 0.3 to 0.7 seconds
Adding these together, we get a total of 15 competitors.
Next, we need to find the number of competitors who reacted in less than 0.3 seconds and were female. From the data, we can see that there are 5 such competitors.
So, the probability that a randomly selected competitor reacted in less than 0.3 seconds and was female is 5/15, which simplifies to 1/3.
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