In a tennis match, on a given point, the player who is serving has two chances to hit the ball in play. The ball must fall in the correct marked box area on the opposite side of the net. A serve that misses the box is called a fault. Most players hit the first serve very hard, resulting in a fair chance of making a fault. If they do make a fault, they hit the second serve less hard and with some spin, making it more likely to be successful. Otherwise, with two misses - a “double fault”- they lose the point. The 2006 men’s champion in the Wimbledon tennis tournament was Roger Federer of Switzerland. During the tournament he made 56% of his first serves. So, hefaulted on the first serve 44% of the time. Given that he made a fault on his first serve, he made a fault on his second serve only 2% of the time. Assuming these are typical of his serving performance, when he serves, what is the probability that he makes a double fault?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
In a tennis match, on a given point, the player who is serving has two chances to hit the ball in play. The ball must fall in the correct marked box area on the opposite side of the net. A serve that misses the box is called a fault. Most players hit the first serve very hard, resulting in a fair chance of making a fault. If they do make a fault, they hit the second serve less hard and with some spin, making it more likely to be successful. Otherwise, with two misses - a “double fault”- they lose the point. The 2006 men’s champion in the Wimbledon tennis tournament was Roger Federer of Switzerland. During the tournament he made 56% of his first serves. So, he
faulted on the first serve 44% of the time. Given that he made a fault on his first serve, he made a fault on his second serve only 2% of the time. Assuming these are typical of his serving performance, when he serves, what is the
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