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. "Nothing makes sense except in the light of evolution"
- Exclusivity. If A and B can't both happen at the same time (in which case we say that A and B are mutually exclusive), then
P(either A or B happens) = P(A happens) + P(B happens)
So, in the case of our pennies, you cannot get hT and Ht at the same time. They are mutually exclusive events. You can either get hT or Ht. We know that the probability of one of them occurring is 1/4. If we want to know the probability of hT or Ht coming up in a toss, P(hT or Ht) = P(hT) + P(Ht) = 1/4+ 1/4 = 1/2
Concomitantly, the P(hT or Ht or Tt or Hh) = 1/4 + 1/4 + 1/4 + 1/4 = 1 (or 100%)
- Independence. If B is no more or less likely to happen when A happens than when A doesn't (in which case we say that A and B are independent), then
P(A and B both happen) = P(A happens) * P(B happens)
So, when you toss the two coins, getting heads on one coin has no effect on whether the second coin comes up heads or tails. The outcome of one coin is therefore independent of the outcome of the second coin. If you want to know the probability of one outcome - say both coins coming up heads at the same time, P(H and h) = P(H) * P(h) = 1/2 * 1/2 = 1/4
- As you increase the number of events in which either A or B can randomly happen ( i.e., either heads or tails), the smaller the deviation from the predicted probability of the event occurring. For example, in 10 coin tosses, you might get 6 heads and 4 tails (deviation = .2 from the predicted outcome) But as you increase the number of trials the closer your total results get to the outcome predicted by probability (50:50) and the smaller the deviation from that probability (deviation = .03, in our trial of 400).