Your friend writes a phone number down on a piece of paper but the last three numbers get smudged after being in your pocket all day long. you decide to randomly choose numbers for each of the three digits. use a sample space to determine whether guessing the first digit correctly and the second digit correctly are independent events.

i don't know and i don't care .

i have learned a great many things from participating in varsity football. it has changed my entire outlook on and attitude toward life. before my freshman year at [high-school], i was shy, had low self-esteem and turned away from seemingly impossible challenges. football has altered all of these qualities. on the first day of freshman practice, the team warmed up with a game of touch football. the players were split up and the game began. however, during the game, i noticed that i didn't run as hard as i could, nor did i try to evade my defender and get open. the fact of the matter is that i really did not want to be thrown the ball. i didn't want to be the one at fault if i dropped the ball and the play didn't succeed. i did not want the responsibility of the team because i was too afraid of making a mistake. that aspect of my character led the first years of my high school life. i refrained from asking questions in class, afraid they might be considered too stupid or dumb by my classmates. all the while, i went to practice and everyday, i went home physically and mentally exhausted.

yet my apprehension prevailed as i continued to fear getting put in the game in case another player was injured. i was still afraid of making mistakes and getting blamed by screaming coaches and angry teammates. sometimes these fears came true. during my sophomore season, my position at backup guard led me to play in the varsity games on many occasions. on such occasions, i often made mistakes. most of the time the mistakes were not significant; they rarely changed the outcome of a play. yet i received a thorough verbal lashing at practice for the mistakes i had made. these occurrences only compounded my fears of playing. however, i did not always make mistakes. sometimes i made great plays, for which i was congratulated. now, as i dawn on my senior year of football and am faced with two starting positions, i feel like a changed person.

over the years, playing football has taught me what it takes to succeed. from months of tough practices, i have gained a hard work ethic. from my coaches and fellow teammates, i have learned to work well with others in a group, as it is necessary to cooperate with teammates on the playing field. but most important, i have also gained self-confidence. if i fail, it doesn't matter if they mock or ridicule me; i'll just try again and do it better. i realize that it is necessary to risk failure in order to gain success. the coaches have always said before games that nothing is impossible; i know that now. now, i welcome the challenge. whether i succeed or fail is irrelevant; it is only important that i have tried and tested myself.

the topic of this essay is how the applicant has matured and changed since his freshman year. he focuses on football. one of the strengths of this essay is that it is well organized. the applicant clearly put time into the structure and planning of this essay. he uses the platform of football to discuss and demonstrate his personal growth and development through the high school years. what he could have done better was spend more time describing himself after he made improvements. as it is, he only tells us about his newfound confidence and drive. this essay would have been stronger had he actually shown us, perhaps by including a story or describing an event where his confidence made a difference

explanation:

i think the first one, it makes the most sense.

ae4