The RSA Novas swimming team is composed of boys and girls in two age categories:

Question

The RSA Novas swimming team is composed of boys and girls in two age categories: 8 and under and 9-10. Each member of the team swims in the 50 Y breast stroke, free style, back stroke, and butterfly events. The distribution of the swimmers by age is shown in the table below. The swimmer's times in seconds are normally distributed and vary by age and gender and are shown below. Note you may assume that each swimmer's time is independent of any other swimmer's times and times for the different strokes are independent of each other. What is the probability a randomly selected swimmer from the team is a boy and in the 8 and under age group? What is the probability a boy swimmer is in the 8 and under age group? Are age and gender independent random variables? Justify

Explanation / Answer

total number =10+15+12+13=50 probability of boy under 8=10/50=1/5 total number of boys= 10+15 probability of boy chosen being under 8= 10/25=2/5=P(under 8 |boy) p(Boy)=25/50 p(under 8 and boy)=12/50 P (under 8)=22/50 if independent then, P (under 8 and boy)= P(boy) P( under8) question is 12/50 equal to(12/50)(22/50)=10/12=5/6 Not true events are independent answer no not independent

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