1. The following table contains the distribution of final grades in an En- glish
ID: 3047843 • Letter: 1
Question
1. The following table contains the distribution of final grades in an En- glish class for 200 students Majors Non-majors A 20 B 22 C 40 D 8 F 6 10 20 50 10 14 If a student is selected at random, what is the probability that the student will (a) be a non-major? (2) (b) Is this a conditional, joint, or unconditional probability? (1) (c) have earned a B? (2) (d) Is this a conditional, joint, or unconditional probability? (1) (e) be a major and earned a C? (2) (f) Is this a conditional, joint, or unconditional probability? (1) (g) be a non-major and earned a B or better? (2) (h) Is this a conditional, joint, or unconditional probability? (1) (i) be a major and earned a D or better? (2)Explanation / Answer
Major Non-Major Total
A 20 10 30
B 22 20 42
C 40 50 90
D 8 10 18
F 6 14 20
Total 96 104 200
(a)
P(Non- Major) = 104/200 = 0.52
(b)
This is unconditional probability
(c)
P(B) = 42/200 = 0.21
(d)
This is unconditional probabilit.
(e)
P(Major & C) = 40/200 = 0.2
(f)
This is joint probability
REASON: It is probability of 2 events occurring together
(g)
P(Non-major & B or better) = P(Non-maor & B) + P(Non-major & A) = 20/200 + 10/200 = 0.1 + 0.05 = 0.15
(h)
This is a joint probability
REASON: It is a probability of 2 events occurring together
(i) P(Major & D or better) = P(Major & D) + P(Major & C) + P(Major & B) + P(Major & A)
= 8/200 + 40/200 + 22/200+ 20/200 = 0.45
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