$3\mathrm{.}26$ Continuing Problem $3\mathrm{.}25,$ organizations once commonly used the last four digits of a

person$$s Social Security number as a unique identifier. $($This is not done so much today

for fear of identity theft.$)$

a$.$ Use the approximation in Equation $(3\mathrm{.}18)$ to calculate the probability of an identifier

collision for k $=10,30,100$ people.

b$.$ What value of k people gives a probability of $0\mathrm{.}5$ of an identifier collision?