Answer :

Given that, X has a binomial distribution.


Also, n = 6 & p = 1/2


And as we know that, p + q = 1


q = 1 – p




Let us define a binomial distribution with x as a variable out of other n variables.


P (X = x) = nCxpxqn-x


Putting values of n, p and q, we get





From the derived result, it can be seen that P (X = x) will be maximum if 6Cx is maximum.


Let us check at what value of x would 6Cx be maximum.


Check at x = 0.




6C0 = 1


Check at x = 6.




6C6 = 1


Check at x = 1.





6C1 = 6


Check at x = 5.





6C5 = 6


Check at x = 2.





6C2 = 15


Check at x = 4.





6C4 = 15


Check at x = 3.





6C3 = 20


Note that at x = 3, 6Cx is maximum.


Hence, we have shown that x = 3 is the most likely outcome.


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