Thea has a key on her calculator marked X. If an integer is displayed, pressing theX key chops off the first digit and moves it to the end. For example, if $6138$ is on the screen, then pressing the X key changes the display to $1386$. Thea enters a positive integer into her calculator, then squares it, then presses the X key, then squares the result, then presses the key again. After all these steps, the calculator displays $243$. What number did Thea originally enter?

Step-by-step explanation:

answer:   35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %,   p(e) = 27 % and = 4 %

and, we have to find out,

but, we know that,

which is the required equation that will use to find the probability of a late departure or an early departure.

therefore,   the probability of a late departure or an early arrival =   35 %