we are asked in this problem to determine the probability of getting at least 6 heads after flipping 10 coins. the sample space of each flip is two that is there is an equal probability of getting a success and a failure. The formula of getting a probability is equal to
F = zPn * p^n *q^(z-n)
we will get the probabilities from 6 to 10.
For 6 successful outcomes
F6 = 10C6 *0.5^6*0.5^4 = 105/512
F7 =10C7*0.5^7*0.5^3 =15/128
F8=10C8*0.5^8*0.5^2=45/1024
F9=5/512
F10=1/1024
The probability of getting at least 6 heads is equal to the sum of the individual probabilities from 6 to 10 that is equal to
Ft = 1/1024+ 5/512+45/1024+15/128+105/512 = 193/512=0.38
