A fair coin is tossed 99 times. If X is the number of times head occur then P [ X = r ] is maximum when r =

Step-by-step solution

The probability of obtaining exactly r heads in 99 tosses of a fair coin is P [ X =r] = 99 r ( 1 2 )⁹⁹ , where 99 r is maximized when r is nearest to n/2 = 49.5 , yielding r = 49 or r = 50 due to symmetry. Equivalently, computing (n+1)p = (99+1) 1 2 = 50 , an integer, confirms that the maximum probability occurs at r = 49 and r = 50 . Among the options, B) 49 gives the maximum probability.