A group of college students is summarized in this table by class and major. (a)
ID: 3300785 • Letter: A
Question
A group of college students is summarized in this table by class and major. (a) If one student is selected, what is the probability of selecting either an English major or a junior? _____ (b) If one student is selected, what is P (senior | math major)? _____ (c) If 3 students are selected randomly, what is the probability of selecting one student from each major? _____ (d) If 3 students are selected randomly, what is the probability of selecting exactly 1 math major? _____ (e) If 3 students are selected randomly, what is the probability of at least 1 physics major? _____Explanation / Answer
Total students = (1 + 2 + 2 + 3 + 1 + 1) = 10
a) P(english major or junior) = P(english major) + P(junior) - P(english major and junior)
= (2+1)/10 + (1+2+2)/10 - (2)/10
= 6/10 or 0.6
b) P(senior | math major) = P(senior and math major) / P(math major)
= (3/10) / ((1+3)/10)
= 3/4 or 0.75
c) P(selecting one studen from each major) = 4C1 * 3C1 * 3C1 / 10C3
= 4*3*3/120
= 3/10 or 0.3
d) P(selecting exactly1 math major) = 4C1 * 6C2 / 10C3
= 4 * 15 / 120
= 1/2 or 0.5
e) P(at least 1 physics major) = 1 - P(no physics major)
= 1 - 7C3/10C3
= 1 - 35/120
= 17/24 or 0.7083
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