Question

Assume that washington, dc license plates contain six numbers, each of which is between 0 and 7, inclusive. what is the probability that a license plate picked at random from the pool of all washington, dc plates contains the same number repeated consecutively –

e.g., 055693, or 387466?

Answer 1

A - picking a plate containing a number repeated consecutively A' - picking a plate with no numbers repeated consecutively

`|\Omega|=8^6=262144\\\\ P(A)=1-P(A')\\ |A'|=8\cdot7^5=134456\\ P(A')=(134456)/(262144)=(16807)/(32768)\\ P(A)=1-(16807)/(32768)=(15961)/(32768)\approx48\%`