Problem 3. (30-3*10 points) 1. A group of twenty female and twenty male students
ID: 3706747 • Letter: P
Question
Problem 3. (30-3*10 points) 1. A group of twenty female and twenty male students are in a room. If eight of the 40 are selected at 2. Alice randomly selects a permutation of (1.2..74. 75. What is the probability that she selects a 3, MATH 261 had two midterm exams, 21% of the students had a score of 80/100 or higher on both Clearly random and put in a row for a picture, what is the probability that the eight are of the same gender? permutation where 75 precedes 7? (Note In the permutation (1. 4.5. 6,3,21, 4 precedes 2.) midterms, 25% had a score of 80/100 or higher on midterm 1, what percentage of the students w had score of 80/100 or higher on midterm I had a score of 80/100 or higher on midterm 2? explain your answer.Explanation / Answer
(1)
No.of.students = 20 female + 20 male
Possibilities to select 8 female = 20 C 8 => choosing any 8 from 20 people
Possibilities to select 8 male = 20 C 8
Total possibilities to select 8 from 40 = 40 C 8
(2) Clearly its 0.5, when we select any permutation out of all available permutations, either 7 preceeds 75 or 75 preceeds 7. Permutations are evenly distributed, hence it is 0.5.
Lets also calculate it mathematically.
Total no.of.permutations = 75 !
Now, we need to choose two places reserved for 7 & 75 => 75 C 2 (always using the first position for 75)
permutating remaining 73 numbers randomly is 73 !
Total permutations with our conditition is 75 C 2 * 73!
Probability = (75 C 2) * 73 ! /( 75 ! ) = 0.5
(3)
Lets take no.of.students be 100 who has got a score of 80 or higher in either M1 or M2.
Percentage of students who got the above score in Midterm 1 = 25% = 25 students
Percentage of students who got the above score in both terms = 21% = 21 students
Lets see the question carefully.. What percentage of the students who had score of 80/100 or higher on midterm 1 had a score of 80/100 or higher on midterm 2...?
Lets reframe this..
What percentage of 25 students had a score of 80/100 on midterm 2?
What percentage of 25 students is 21 students.?
(because 21 students scored 80 in both..)
=> (21/25) % = 84%
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