Question

Event A and B are independent of each other...
What does independent mean here? How would it change if it said dependent. The full question continues as:
The probability of event A occurring is 3x as likely as event B occurring. The probability that neither event A nor event B will occur is 7/27. What is the probability of event A occurring?

Answer 1

If two events A and B are independant then
P(A intersection B)=P(A)P(B)

Answer 2

Just take P(B) as x P(A)=3x.
Apply the condition and solve for x.

Answer 3

phi the venn diagram i think is wrong, independant does not mean that it has no element in common.

Answer 4

1-P(A union B)=7/27.
P(A union B)=20/27.
P(A)+P(B)-P(A intersection B)=20/27.
x+3x-3x^2=20/27.
Solve for x.

Answer 5

@Phi, 15/27 is not a possible answer.
Neither of you are making very much sense. I don't understand what shank means by intersection or union

Answer 6

yep, thanks !

Answer 7

Definition: Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.

Some other examples of independent events are:

Landing on heads after tossing a coin AND rolling a 5 on a single 6-sided die.
Choosing a marble from a jar AND landing on heads after tossing a coin.
Choosing a 3 from a deck of cards, replacing it, AND then choosing an ace as the second card.
Rolling a 4 on a single 6-sided die, AND then rolling a 1 on a second roll of the die.
http://www.mathgoodies.com/lessons/vol6/independent_events.html

Answer 8

Thanks directrix. Could you give some examples of dependent then?

Answer 9

how can you have a union or intersection of a probability? I thought that was in sets.

Answer 10

Please help me.

Answer 11

shankvee definitely has the right idea here