Is there a relationship between gender and relative finger length? To find out, we randomly selected 452 U.S.

Is there a relationship between gender and relative finger length? To find out, we randomly selected 452 U.S. high school students who completed a survey. The two-way table summarizes the relationship between gender and which finger was longer on the left hand (index finger or ring finger)

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Suppose we randomly select one of the survey respondents. Define events R: ring finger longer and F: female. Find P(R|F). Interpret this value in context.

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Definition conditional probability: $P\left(B|A\right)=\frac{P\left(A\cap B\right)}{P\left(A\right)}=\frac{P\left(AandB\right)}{P\left(A\right)}$ Solution R=ring finger longer F=female We note that the table contains information about 452 students (given in the bottom right corner of the table). Moreover, 212 of the 452 students are female, because 212 is mentioned in the row ” Total” and in the column ”Female” of the table. The probability is the number of favorable outcomes divided by the number of possible outcomes: $P\left(F\right)=\frac{\text{# of favorable outcomes}}{\text{# of possible outcomes}}=\frac{212}{452}$ Next, we note that 82 of the 452 students are females with a longer ring finger, because 82 is mentioned in the row ” Ring finger” and in the column ”Female” of the given table. $P\left(RandF\right)=\frac{\text{# of favorable outcomes}}{\text{# of possible outcomes}}=\frac{82}{452}$ Use the definition of conditional probability: $P\left(R|F\right)=\frac{P\left(RandF\right)}{P\left(F\right)}=\frac{82/452}{212/452}=\frac{42}{212}=\frac{41}{106}\approx 0.3868=38.68$ 38.68% of the female students have a longer ring finger.