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by Tauqeer » Sat Apr 18, 2009 12:22 pm
Why is the probability that on at least one of the tosses the coin will not turn up heads = 1?
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by DanaJ » Sun Apr 19, 2009 2:23 am
It's not 1, it's (1 minus the probability that the coin will turn up heads on all three tosses).
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by T_A_M » Sun Apr 19, 2009 2:49 am
Yes I know you have to minus the probability of the 3 heads (from 3 tosses), from 1. But where did the 1 come from and how is it calculated?
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by DanaJ » Sun Apr 19, 2009 4:15 am
Your basic formula for probabilities is:
number of favorable cases
------------------------------
all possible cases

This fraction is usually smaller than 1. One example would be the coin toss: say you consider heads a favorable case. Then out of two possible cases (heads or tails), there is only one favorable case (heads). This is why the probability of getting heads when tossing a coin is 1/2.

When the probability of an event is 1, then that even is CERTAIN: the probability that I'll die some day is a certainty, so the probability of that particular event is 1. This happens when the number of favorable cases is equal to the number of possible cases. It's the same as saying that you are satisfied with whatever outcome of a coin toss.
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