How does C(n) = P(down)[C( n - 1 ) + C(n) + k (n)] + P(same)[(C(n) + k(n)] + P(break)[C(n) + R + k(n)] + P(up)k(n)
become
C(n)[1-P(down)-P(same)-P(break) =
P(down)C(n-1) + P(break)R + k(n) ?

Please explain to me the factorisation process of the C(n) terms as thoroughly as possible and the summation of the k(n) terms as thoroughly as possible.

Either I have forgotten how factorisation works or I dont understand the maths of Markov chain & recurrence relations, or the poster skipped a lot of steps in his mathematical presentation.

Please help.

2a+7+4ahow many terms? how many variables? any like terms? yes noif yes, which ones? what are the coefficients? any constants? yes noif yes, which ones? simplify the expression by combining like terms and constants: how many terms now?

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.

Solve this problem! extra ! 3025/5.5 = a/90.75 / = fraction