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If the two events are independent and equally likely, and the probability that at least one of them occurs is 0.25, what is the probability of either event?

I think that A and B two independent event and $P(A)=P(B)=a$

If at least one of them occurs is 0.25,

$P(A) + P(A) + P(A \cap B) = 0.25$

$ a + a+ a^2 = 0.25$

$ 4a^2 + 8a+4 -5 = 0$

$ 4a^2 + 8a+4 = 5$

$(2a+2)^2 = 5$

so result is equal to a

$ a = \frac{\sqrt{5} - 2}{2}$

Is this solution right?

Thanks in advance.

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1 Answer 1

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The probability that at least one occurs is $P(A) + P(B) - P(A \cap B)$. You have to subtract, or you're double-counting the cases where both occur. Think about this when $a = 0.5$. The chance of getting at least one HEAD in two coin flips is $0.75$, not $1.25$, right?

Now try to figure out the rest...you're on the right track.

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