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I'm surprised you didn't come across complements before you encountered this problem. You could also take the complements of the information given: If P[AuB] = 0.7, then the complement is P[AuB]' = 1 - P[AuB] = 1 - 0.7 = 0.3 = P[A'nB']. And the complement of P[AuB'] is P[A'nB] = 0.1.
If P[A] = P[AnB] + P[AnB'], then P[A'] = P[A'nB] + P[A'nB'].
P[A'] = 0.1 + 0.3 = 0.4
P[A] = 1 - P[A'] = 1 - 0.4 = 0.6.
Thank you RossMoney34 and NoMoreExams for your persistence and patience. I understand now.
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