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) = nCxpxqn-x
Where x = 1, 2, 3, …, n
Here, p = probability of getting a head.
And q = probability of getting a tail.
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
Now, putting n = 8 & x = 7. We get
Now, putting n = 8 & x = 8. We get
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 .
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