If you flip a coin nine times and get nine heads in a row, is the tenth throw more likely to produce a head or tail?
Those who don't understand the principles of probability might be tempted to say, "the next one must be a tail," but, of course, the probability is always the same for each throw (assuming no trickery or cheating is involved). The probability of throwing a head is 1/2 (or 1 in 2) and the probability of throwing a tail is also 1/2 (1 in 2) because there are two equally likely outcomes to flip a coin.
However, it is easy to see why people get confused, because the probability of throwing ten heads in a row is very small (1 in 1024). Why? Because the probability of a sequence of events is the result of multiplying the probabilities of each event together.
The probability of throwing one head is 1/2. The probability of throwing two heads is 1/2 X 1/2 = 1/4. The probability of throwing three heads is 1/2 X 1/2 X1/2 =1/8...and so on. The probability of throwing ten heads is 1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 = 1/1024.
When you throw dice, the chance of throwing a 3 is 1 in 6 or 1/6 because there are six equally likely outcomes to the throw of a dice (1, 2, 3, 4, 5, 6). The sum of all possible outcomes must always add up to 1. When you throw two or more dice and add them together, the probability of getting a two (1 +1) is 1/6 X 1/6 = 1/36 but the probability of getting a seven is 1/6 because there are six ways of doing it out of a possible 36 outcomes: (1+6), (2+5), (3+4), (4+3), (5+2), and (6
