In a board game, you must roll two 6-sided number cubes. you can only start the game if you roll a 3 on at least one of the number cubes. suppose you rolled the two number cubes 100 times, would you expect at least one 3 more or less than 34 times? explain.

Miranda is braiding her hair. then she will attach beads to the braid. she wants 1_3 of the beads to be red. if the greatest number of beads that will fit on the braid is 12,what other fractions could represent the part of the beads that are red?

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

Abag contains 3 red marbles, 2 blue marbles, and 2 green marbles. one marble is picked, then another marble. assume that the selections are made with replacement. a) find the probability of picking two red marbles with replacement. b) find the probability of picking a red marble and a blue marble. assume the selections are made without replacement. c) find the probability of picking two red marbles without replacement. d) find the probability of picking a red marble and a blue marble without replacement.