P(A and C) = 0.33, P(B and C) = 0.28, ……………………………………………………….(1)
P(A and D) = 0.18, P(B and D) = 0.14, ……………………………………………………….(2)
P(A and E) = 0.04, P(B and E) = 0.03, ……………………………………………………….(3)
Row totals represent: P(C) = 0.61, P(D) = 0.32, P(E) = 0.07, ………………………………(4)
Column totals represent: P(A) = 0.55, P(B) = 0.45. …………………………………………(5)
P(A or B) = P(A U B) = P(A) + P(B) - P(A ⋂ B), where P(A ⋂ B) represents P(A and B) .. (6)
Part (a)
P(B or C) = P(B) + P(C) - P(B and C)
= 0.45 + 0.61 – 0.28 [ (5), (4) and (1)]
= 0.78 ANSWER
Part (b)
P(B or D) = P(B) + P(D) - P(B and D)
= 0.45 + 0.32 – 0.14 [ (5), (4) and (2)]
= 0.63 ANSWER
Part (c)
P(A or E) = P(A) + P(E) - P(A and E)
= 0.55 + 0.07 – 0.04 [ (5), (4) and (3)]
= 0.58 ANSWER
Part (d)
P(A or B) = P(A) + P(B) - P(A and B)
= 0.55 + 0.45 – 0
= 1.0 ANSWER
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