BACHELOR OF SCIENCE (B.Sc.) IN SCIENCE & ENGINEERING DISCIPLINES Spring Semester

Question

BACHELOR OF SCIENCE (B.Sc.) IN SCIENCE & ENGINEERING DISCIPLINES Spring Semester (2018) MIDTERM EXAMINATION Course MATH-223 Probabilitv and Statistical Inference Student Name Student ID Professor Name Dr. Gary Miller Date of Exam: 14 March 2018 Time and Duration: 1 hour and 15 minutes 1 In a small group of students there are 3 who take the physics course, 4 who take the course, and 7 who take the safety course. There are two students that take both mathematics a mathematics physics, two that take both mathematics and health, and two that take both physics and heath. There is only one student that takes all three of these courses. How many students are there in t 2 We have 3 people and 3 rooms. How many ways can we put exactly one person in each room? 3 otal? The grades given to 41 students are A, B,C,D, or F. How many combinations of grades are possible? 4 Two dice are thrown. What is the probability that at least one six appears? Pr(B)-0.6, Pr(Ba) = 0.2, Pr(,) n B2 n B,-0, Pr(AI&J; = 0.3, Pr(A|B2)-0.1, and Pr(A] B3)-0.1 = 0.2, and B11

Explanation / Answer

#1.
P = 3, M = 4, H = 7
M and P = 2, M and H = 2, P and H = 2
M and P and H = 1

Total number of students = 3 + 4 + 7 - 2 -2 - 2 + 1 = 9

#2.
Total number of ways = 3C1 * 2C1 * 1C1 = 6

#3.
A student can have any of the 6 possible grades.
Hence total possible combinatinos are 6^41

#4.
There are total 36 possible outcomes out of which there are 11 outcomes where there is at least one 6 appears

Hence required probability = 11/36

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