Consider a collection of envelopes consisting of 3 red envelopes​, 1 blue envelope​, 2 green envelopes​, and 3 yellow envelopes. If two envelopes are selected at​ random, with​ replacement, determine the probability that at least one envelope is a red envelope.

The probability that at least one of the envelopes is red is 1/9.

Step-by-step explanation:

There are a total of 9 envelopes. If two are selected at random with replacement the probability for both envelopes is 3 / 9 or 1/3. Since there are two you would do 1/3 * 1/3 to get 1/9.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.