A coin is tossed eight times What is the probability of gett

Solution

Tossing a coin is a binomial experiment, with p = 0.5
when a binomial experiment is repeated over a number of times it becomes a Bernoulli\'s experiment (would love to elaborate on what this experiment is and it\'s details, ask for it in the comments if u want me to).
Let X be number a discrete random variable which denotes the number of heads obtained in \'n\' (in our case \'n\' is 8) number of tosses.
The general form for probability of r.v. X is :-
P(X = x) = nCx p^x q^(n-x)      ...................(here \'x\' takes values from 0 to n, n = 8 and q = (1-p) )
therefore, P(X=x) = 8Cx (0.5)^x (0.5)^(8-x)
so our distribution will be, (these following values are an approximate)
P(X=0) = 0.00390625
P(X=1) = 0.03125
P(X=2) = 0.109375
P(X=3) = 0.21875
P(X=4) = 0.2734375
P(X=5) = 0.21875
P(X=6) = 0.109375
P(X=7) = 0.03125
P(X=8) = 0.00390625

what you are trying to find is is probability of getting at least one heads, ie probability of getting 1 heads or 2 heads or 3 heads or 4 heads or 5 heads or 6 heads or 7 heads or 8 heads as the result of tosses and by fundamental principal of counting all probabilities from P(X=1) to P(X=8) are to be added. This can be represented in probability terms as, P(X>=1).
Final answer P(X>=1) = 0.03125 + 0.109375 + 0.21875 + 0.2734375 + 0.21875 + 0.109375 + 0.03125 + 0.00390625 = 0.99609375

Bonus lazy man tip (better to use this),
P(X>=1) = 1 - P(X<1) = 1 - P(X = 0)= 1 - 0.00390625 = 0.99609375