Question

When three unbaised coins are thrown, the probability of getting exactly two tails and probability of getting at least two tails are the roots of a Quadratic equation.Find the Quadratic equation.

Answer 1

n(s)={H,T} x {H,T} x {H,T}
={H,H,H},{H,H,T},{H,T,H},{H,T,T}{T,H,H},{T,H,T},{T,T,H},{T,T,T}=8

now events of exactly getting two tails
n(E)={H,T,T},{T,H,T},{T,T,H}
=3
now,
p(E)=n(E)/n(s)=3/8

again events of getting at least two tails
n(E)={H,T,T},{T,H,T},{T,T,H},{T,T,T}=4

now ,
p(E)=n(E)/n(s)=4/8

according to question ,
3/8 and 4/8 are the roots of quadratic
hence, quadratic equation :-
(x-3/8)(x-4/8)=0

x^2-7x/8+12/64=0

64x^2-56x+12=0

hence 64x^2-56x +12=0. is quadratic equation.