Question

his contingency table describes 200 business students.

	Major
Gender	Accounting (A)	Economics (E)	Statistics (S)	Row Total
Female (F)	44	27	26	97
Male (M)	48	30	25	103
Column Total	92	57	51	200

Find each probability. (Round your answers to 4 decimal places.)

a.	P(A)
b.	P(M)
c.	P(A ∩ M)
d.	P(F ∩ S)
e.	P(A | M)
f.	P(A | F)
g.	P(F | S)
h.	P(E U F)

Answer 1

Using given contingency table we find the following probabilities,

a) P(A) = 92/200 = 0.46

=> P(A) = 0.46

b) P(M) = 103/200 = 0.515

=> P(M) = 0.515

c) P(A ∩ M) = 48/200 = 0.24

=> P(A ∩ M) = 0.24

d) P(F ∩ S) = 26/200 = 0.13

=> P(F ∩ S) = 0.13

e) P(A | M) = 48/103 = 0.4660

=> P(A | M) = 0.4660

f) P(A | F) = 44/97 = 0.4536

=> P(A | F) = 0.4536

g) P(F | S) = 26/51 = 0.5098

=> P(F | S) = 0.5098

h) P(E U F) = P(E) + P(F) - P(E ∩ F)

=> P(E U F) = (57/200) + (97/200) - (27/200)

=> P(E U F) = (57 + 97 - 27)/200

=> P(E U F) = 127/200

=> P(E U F) = 0.635

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