If we toss 9 fair coins, then we can get at least one head and one tail in 510 ways.
What is Probability?
Probability is the possibility to occurrence of an event.
What is Fair Event?
An event is fair if probabilities of all possible different outcomes for that event is equal.
The total number of outcomes if we toss n number of coin is given by
[tex] = {2}^{n} [/tex]
Here in the given problem, we toss 9 fair coins so the number of total possibilities
[tex] = {2}^{9} = 512[/tex]
Now if all 9 coins are heads or all 9 coins are tail then only we cannot obtain the event that to obtain at least one head and one tail.
so number of ways to obtain all heads = 1
number of ways to obtain all tails = 1
Hence the number of ways to obtain at least one head and one tail is = 512 - (1 + 1) = 512 - 2 = 510
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