When we roll one die, we have a 1 in 6 probability of getting any particular number on the die. when we roll a pair of dice, there are 36 different pairs that can be produced, yet only 11 actual distinct values. explain how the probability associated with the roll of each individual die in the pair explains the higher variability in the total outcome of the roll of each pair. how do the concepts of permutations and combinations apply to this example? discuss how the notion of degree of freedom can be used to illustrate the accumulating results of a set of dice rolls.

To find the extreme values of a function f(x.y) on a curve x-x(t), y y(t), treat f as a function of the single variable t and use the chain rule to find where df/dt is zero. in any other single-variable case, the extreme values of f are then found among the values at the critical points (points where df/dt is zero or fails to exist), and endpoints of the parameter domain. find the absolute maximum and minimum values of the following function on the given curves. use the parametric equations x=2cos t, y 2 sin t functions: curves: i) the semicircle x4,y20 i) the quarter circle x2+y-4, x20, y20 b, g(x,y)=xy

Plz a. s. a. p.the table shows the number of male and female contestants who did not win a prize. what is the probability that a randomly selected contestant won a prize, given that the contestant was female? write the probability as a percent. round to the neares tenth, if needed.

Find an bif a = {3, 6, 9, 12) and b = {2, 4, 6, 8, 10).