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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 Female Less than 0.3 seconds 3 5 0.3 to 0.7 seconds 5 2 What is the probability that a randomly selected competitor reacted in less than 0.3 seconds and was female? Simplify 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.\newline\begin{tabular}{|l|c|c|}\newline\cline { 22 - 33 } & Male & Female \\\newline\hline Less than 00.33 seconds & 33 & 55 \\\newline\hline 00.33 to 00.77 seconds & 55 & 22 \\\newline\hline\newline\end{tabular}\newlineWhat is the probability that a randomly selected competitor reacted in less than 00.33 seconds and was female?\newlineSimplify any fractions.\newline□ \square

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Q. 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.\newline\begin{tabular}{|l|c|c|}\newline\cline { 22 - 33 } & Male & Female \\\newline\hline Less than 00.33 seconds & 33 & 55 \\\newline\hline 00.33 to 00.77 seconds & 55 & 22 \\\newline\hline\newline\end{tabular}\newlineWhat is the probability that a randomly selected competitor reacted in less than 00.33 seconds and was female?\newlineSimplify any fractions.\newline□ \square
  1. Calculate Total Competitors: First, let's find the total number of competitors. We add up all the males and females in both reaction time categories.\newlineTotal competitors = (33 males with <0.3s<0.3\text{s}) + (55 females with <0.3s<0.3\text{s}) + (55 males with 0.3−0.7s0.3-0.7\text{s}) + (22 females with 0.3−0.7s0.3-0.7\text{s})\newlineTotal competitors = 3+5+5+23 + 5 + 5 + 2\newlineTotal competitors = 1515
  2. Find Females with <0.3s<0.3s Reaction Time: Now, we need to find the number of competitors who are female and reacted in less than 0.30.3 seconds.\newlineNumber of females with <0.3s<0.3s reaction time = 55
  3. Calculate Probability: To find the probability, we divide the number of females with <0.3s<0.3s reaction time by the total number of competitors.\newlineProbability = Number of females with <0.3s<0.3s reaction time / Total competitors\newlineProbability = 515\frac{5}{15}
  4. Simplify Fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 55.\newlineProbability = (5÷5)/(15÷5)(5 \div 5) / (15 \div 5)\newlineProbability = 1/31 / 3

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