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Determine if the following situation satisfies all of the conditions required for a binomial probability experiment. If it does, then specify how each of the conditions are satisfied. If it does not, then specify which conditions are not met.Make sure to provide sufficient justification for your answers by stating how each condition is met in context of the scenario given.    Scenario: A student walks into class after not showing up the week before and finds out there is a multiple choice quiz in class that day. Since they were not in class during the previous week, all they can do is randomly guess on each question. There are 25 questions on the quiz and all of the questions have 5 possible answers (A,B,C,D, or E). The number of correct answers on the quiz will be recorded. 

Suppose you roll a standard 6-sided die one time. What is the probability that you would roll a number greater than 1? Recall that the sample space for this scenario would be .   Make sure to type in your answer as a decimal rounded to 2 decimal places. For example, if you thought the answer was 0.12345 then you would type in 0.12. 

Suppose you roll a standard 6-sided die and you recorded the number of times that you ended up rolling an even number. Find the probability that you would get no less than 3 even numbers out of 5 rolls of the dice. Make sure to type in your answer rounded to 2 decimal places. For example, if you thought the answer was 1.23456, then you would type in 1.23.

A professor was interested in comparing how well her students performed on their midterm and final exams in her calculus course. She randomly sampled 7 students from her class and recorded their midterm and final exam grades which are shown in the table below. Midterm and Final Exam Grade Comparisons Student X=Midterm Exam Y=Final Exam Student 1 75 86 Student 2 73 77 Student 3 87 70 Student 4 90 92 Student 5 72 95 Student 6 84 93 Student 7 91 89   Use this information to calculate the y-intercept of the least squares regression line.  Make sure to type your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 98.76543 then you would type in 98.765.

Suppose you have a standard deck of 52 playing cards and you randomly select 1 card and record whether or not the card that you drew was a “club”. You then return to the card back to the deck and repeat this process a total of 6 times so that you end up drawing 6 cards total. Find the probability that more than 1 of the 6 cards that you drew were clubs.  Make sure to type in your answer rounded to 2 decimal places. For example, if you thought the answer was 1.23456, then you would type in 1.23. Note: In a standard deck of playing cards, 13 of them are clubs and 39 of them are not. 

Consider the table below that shows how many students from each year are in each of the Hogwart’s houses. Use this information to answer the probability question that follows.  Hint: I would recommend finding the totals for each row and column first.  Probability Table Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Ravenclaw 30 38 34 33 39 31 35 Hufflepuff 36 33 29 37 39 35 34 Gryffindor 32 36 41 32 33 35 35 Slytherin 34 32 36 39 33 32 31   Find the probability that a randomly selected student is from Slytherin.    Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was , then you would type in 0.431.

Consider the table below that shows how many students from each year are in each of the Hogwart’s houses. Use this information to answer the probability question that follows.  Hint: I would recommend finding the totals for each row and column first.  Probability Table Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Ravenclaw 30 38 34 33 39 31 35 Hufflepuff 36 33 29 37 39 35 34 Gryffindor 32 36 41 32 33 35 35 Slytherin 34 32 36 39 33 32 31   Find the probability that a randomly selected student is in year 6 given that they are in Hufflepuff.    Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was , then you would type in 0.431.

Consider the table below that shows how many students from each year are in each of the Hogwart’s houses. Use this information to answer the probability question that follows.  Hint: I would recommend finding the totals for each row and column first.  Probability Table Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Ravenclaw 30 38 34 33 39 31 35 Hufflepuff 36 33 29 37 39 35 34 Gryffindor 32 36 41 32 33 35 35 Slytherin 34 32 36 39 33 32 31   Find the probability that a randomly selected student is in year 3 and from Hufflepuff.    Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was , then you would type in 0.431.

Suppose you have a standard deck of 52 playing cards and you randomly select 1 card and record whether or not the card that you drew was a “club”. You then return to the card back to the deck and repeat this process a total of 6 times so that you end up drawing 6 cards total. Find the probability that less than 4 out of the 6 cards that you drew were clubs.  Make sure to type in your answer rounded to 2 decimal places. For example, if you thought the answer was 1.23456, then you would type in 1.23. Note: In a standard deck of playing cards, 13 of them are clubs and 39 of them are not. 

Suppose you flip a coin in the air one time and record the result (Heads or Tails) as it lands. Then you flip the coin again and record the result a second time. Find the following probability: What is the probability that you get “Heads” on both coin tosses?   Make sure to type in your answer as a decimal rounded to 2 decimal places. For example, if you thought the answer was 0.12345 then you would type in 0.12.