A fair coin is thrown in the air six times. If the coin lands with the head up on the first five
tosses, what is the probability that the coin will
land with the head up on the sixth toss?

The probability of heads on any flip is 1/2

which means(1/2)^6 which gives 1/64 or in decimal 0.015625

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.