An unbiased coin

Let x be the number of heads in the tosses.

Let n be the total number of tosses.

Then, binomial distribution is given by

P (X = x) = ⁿC_xp^xq^n-x

Where x = 1, 2, 3, …, n

Here, p = probability of getting a head.

And q = probability of getting a tail.

Then,

We need to find the probability of getting at least 6 head.

Then, x = 6, 7, 8 [∵ there are 8 number of tosses]

First, putting n = 8 & x = 6. We get

…(i)

Now, putting n = 8 & x = 7. We get

…(ii)

Now, putting n = 8 & x = 8. We get

…(iii)

The probability of getting at least 6 heads is given by

Probability = P(6) + P(7) + P(8)

Substituting values in (i), (ii) & (iii) in above equation. We get

Thus, the probability of getting at least 6 heads is .