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If you flip a fair coin four times, what is

explanation :
Consider a general tax of flipping N coins and the probability of precisely K times the heads are up. Let ‘s use a symbol P ( N, K ) for this probability.
Knowing this, we can use the leave to evaluate


which will answer the interview of what is the probability of getting heads at lease 2 times out of flipping a mint 4 times.
Since there are only 2 outcomes from a single flip, head or tail, for N flips we can get


unlike outcomes.
The outcomes we are concerned in are those that contain precisely K heads and


tails in any order. That is where combinatorics will come handy.
Any result of the random experiment of flipping a coin N times can be represented as a string of N characters, each one being a letter H ( to designate that the comparable flip resulted in a head ) or T ( if it was a buttocks ).
The number of outcomes with precisely K heads out of N flips is the number of strings of the length N consist of characters H and T, where H occurs K times and T occurs


times in any order.
This number is, obviously, a number of combinations of K items out of N, which symbolically is represented as


( there are other notations as well ) and is equal to


For all the hypothesis behind this and early formulas of combinatorics we can refer you to a correspond part of the advanced course of mathematics for high educate at Unizor.
The probability of having K heads out of N flips is equal to the ratio of the number of “ successful ” outcomes ( those with precisely K heads ) to a sum number of outcomes mentioned above :


now we can calculate the probability of at least two heads out of four flips ( do n’t forget that


by definition ) :




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