Probability question?

Question

Two events are independent with P(A) = 0.25 and P(B) =0.6. What is the probability of A or B?

Answer 1

The probability of [A and B] is 0.25 x 0.6 = 0.15.

The probability of [neither A nor B] is (1-0.25) x (1-0.6) = 0.3.

The only other possibility is [either A or B], which is one minus the sum of the other two probabilities, which is 1 - (0.15 + 0.3) = 0.55.

Using the logic of the first answer, if there were an event "C" with a probability of 0.5, then the probability of A or B or C would be 0.25 + 0.6 + 0.5 = 1.35, which is more than 100%, which is absurd.

ADDENDUM:

Looking at this another way, there are only four possibilities for the turn of events described by the questioner:

1) A and B occur
2) A and B do not occur (neither A nor B occur)
3) A occurs, but not B
4) B occurs, but not A

The probability of two independent events occuring equals the product of their individual probabilities: 0.25 x 0.6 = 0.15.

The probability of an event not occurring equals one minus the probability it will occur: NOT A = 1 - 0.25 = 0.75; NOT B = 1 - 0.6 = 0.4.

The probability of two independent events not occurring is the product of the individual probabilities they will not occur: 0.75 x 0.4 = 0.3.

Now we've eliminated the first two scenarios. Since there are only four possibilities for scenarios occurring, the probability of the remaining two scenarios occurring is one minus the sum of the first two scenarios occurring: 1 - (0.15 + 0.3) = 0.55.

I stand by my answer.

Answer 2

P(AUB) = P(A) + P(B) - P(A∩B)
= P(A) + P(B) - P(A) P(B) because A & B are independent.
= 0.25 + 0.6 - (0.25*0.6)
= 0.7

d:

Edit:
http://en.wikipedia.org/wiki/Independent_events
Thus the assumption I made here is that the events A & B are mutually independent.
In the case where P(A∩B) = 0 we say that A & B are mutually exclusive.
These two ideas are different from each other.

The case where you get either A or B but not together, that is called the symmetric difference.
http://en.wikipedia.org/wiki/Symmetric_difference

Edit2:
The additional information is already the fact that they are independent.

Answer 3

If the events are mutually exclusive
P(A or B) = 0.85
If they are not mutually exclusive,
0.6 ≤ P(A or B) < 0.85
and additional information is needed to determine it exactly.

Answer 4

.25+.6-(.25*.6)=.7

Answer 5

dc's explanation is good