Let's say A has a 0.7 probability, and B has 0.6, and are independent. The compound probabilities are gotten by multiplying the individual ones:
Neither: 0.3 * 0.4 = .12
A, not B: 0.7 * 0.4 = 0.28
B, not A: 0.3 * 0.6 = 0.18
Both: 0.7 * 0.6 = 0.42
Now let's say that they're not independent; in fact, B absolutely requires A. You'd get something like:
Neither: 0.3 (this is reduced to the chance of not A)
B, not A: 0 (B can't happen without A)
Both: 0.6 (only other probability with B, has to make up the 0.6)
A, not B: 0.1 (simply what's left to sum to 1.0)
Concrete examples of independent events: (fair) coin tosses -- the chance to come up heads is always the same, no matter the prior result. Related events: being dealt a face card in blackjack, and winning the hand -- whatever your normal chance of winning a hand, the odds of winning that particular hand just went up.
Neither: 0.3 * 0.4 = .12 A, not B: 0.7 * 0.4 = 0.28 B, not A: 0.3 * 0.6 = 0.18 Both: 0.7 * 0.6 = 0.42
Now let's say that they're not independent; in fact, B absolutely requires A. You'd get something like:
Neither: 0.3 (this is reduced to the chance of not A) B, not A: 0 (B can't happen without A) Both: 0.6 (only other probability with B, has to make up the 0.6) A, not B: 0.1 (simply what's left to sum to 1.0)
Concrete examples of independent events: (fair) coin tosses -- the chance to come up heads is always the same, no matter the prior result. Related events: being dealt a face card in blackjack, and winning the hand -- whatever your normal chance of winning a hand, the odds of winning that particular hand just went up.