We flip a fair coin 10 times. what is the probability that we get heads in at least 6 of the 10 flips?

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