A fair coin is tossed for a fixed number of times. If probability of getting 7 heads is equal to probability of getting 9 heads, then probability of getting 2 heads is

Step-by-step solution

p = probability of getting head = 1 2 and q = probability of not getting head 1 2 P ( X = x )= ^ n C _ x ( 1 2 )^ x ( 1 2 )^ n - x As per data given, we write aligned & P ( x =7)= P ( x =9) & ^n C ₇ ( 1 2 )^7 ( 1 2 )^ n -7 = ^ n C ₉ ( 1 2 )^9 ( 1 2 )^ n -9 & ^ n C ₇= ^ n C ₉ & n =16 aligned when x=2 , we get P ( x =2)= ¹⁶ C ₂ ( 1 2 )^2 ( 1 2 )¹⁴= 16 15 2 ( 1 2 )¹⁶= 15 (2)¹³