Answer :

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.



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 .


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