# 2 Independent events probability

Probability is by far not my strong suit and I need to solve this question thoroughly. So if somebody could help me with this one:

A firm z is considering acquiring two different firms: firm A and firm B. It believes it will acquire firm A with probability 0.6 and firm B with probability 0.1. Assuming that those two events are independent, find the probability that Z acquires either firm.

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• Try to consider every possibility: A and B, A but not B, B but not A, neither A nor B. Calculate their probabilities and figure out which add up to the requested probability. – SmileyCraft Oct 10 '18 at 18:54

Let $$A^c$$ be the event that the company will not acquire the firm A and $$B^c$$ analogously for firm B.
Then $$P(A^c \cap B^c) = P(A^c)P(B^c)=(1-0.6)(1-0.1)=0.4 \times 0.9=0.36$$ where the first equality follows from the independency.
$$\mathbf {Edit}:$$ I misread the question, but this is still a good hint for what you actually need to compute.
Let $$A$$ be the event acquiring firm A and $$B$$ be the event acquiring firm B. The probability of acquiring either firm is: $$\mathbb{P}(A \cup B) = \mathbb{P}(A) + \mathbb{P}(B) - \mathbb{P}(A \cap B)$$ Since events A and B are independent $$\mathbb{P}(A \cap B) = \mathbb{P}(A) \cdot \mathbb{P}(B)$$. The rest is putting the numbers...