heeeeeeeeeeelp math
posted by lin .
A strip of 41 squares is numbered 0,1,2,…,40 from left
to right and a token is placed on the square marked 0. Pinar
rolls a pair of standard sixsided dice and moves the token right a number of squares equal to the total of the dice roll. If Pinar rolls doubles, then she rolls the dice a second time and moves the token in the same manner. If Pinar gets doubles again, she rolls the dice a third time and moves the token in the same manner. If Pinar rolls doubles a third time she simply moves the token to the square marked 36.
The expected value of the square that the token ends on can be expressed as a/b where a and b are coprime positive
integers. What is the value of a+b.

Solve using a probability tree.
First calculate the outcomes with distinct rolls for a sum of P(x)=30/36.
For simplicity, the probability is multiplied by 36 to use integers.
sum=x 36*P(x) x*36*P(x)
3 2 6
4 2 8
5 4 20
6 4 24
7 6 42
8 4 32
9 4 36
10 2 20
11 2 22
Sums of 2 and 12 are always doubles so they do not appear in the table above.
Doubles have a probability of 6/36=1/6, so the above table should be multiplied by (1+1/6) to account for the first double then nondoubles.
Getting doubles twice has a probability of (6/36)², so we multiply the above probabilities by (1+1/6+1/36)=43/36 for all cases except 3 doubles.
3 doubles have a probability of (1/6)³, so the complete table becomes:
sum=x P(x) x*P(x)
3 43/648 43/216
4 43/648 43/162
5 43/324 215/324
6 43/324 43/54
7 43/216 301/216
8 43/324 86/81
9 43/324 43/36
10 43/648 215/324
11 43/648 473/648
36 1/216 1/6
for a sum of probabilities of 1.
Expected value of outcome
=Σ x*P(x)
=1541/216 
^Wrong a+b is < 1000

The way I interpreted the question is that she does not move at all if she rolls doubles.
After rereading, it looks like that when she rolls doubles, she moves the token before rolling again, and on the third double, she advances it to 36.
If this latter interpretation is correct, it will be necessary to adjust the calculations for the new situation.
Try the same principle as above for the new situation. If you don't get the right answer, post what you've got and we'll take it from there. 
even with the latter interpretation i still cannot get a result of a+b<1000. could you try working on it?

122
Respond to this Question
Similar Questions

Math
Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). 
Math
A student rolls three standard sixsided dice. What is the probability that the sum of the numbers that come up will be 18? 
math
A token is placed on the corner square of a 3×3 chess board. The token is moved either up, down, left, or right, with equal probability. If the token would move off the edge of the board it "wraps around'' the board and moves to the … 
heeeeeelpm math
A strip of 41 squares is numbered 0,1,2,…,40 from left to right and a token is placed on the square marked 0. Pinar rolls a pair of standard sixsided dice and moves the token right a number of squares equal to the total of the dice … 
Math (please help steve)
Brilli the ant randomly placed a token into a square on a 2×100 chessboard according to a probability distribution P. The token is then moved uniformly at random to one of the horizontally, vertically, or diagonally adjacent squares. … 
math (please help steve)
Brilli the ant randomly placed a token into a square on a 2×100 chessboard according to a probability distribution P. The token is then moved uniformly at random to one of the horizontally, vertically, or diagonally adjacent squares. … 
math
A token is placed on the leftmost square in a strip of four squares. You are allowed to move the token left or right along the strip by sliding it a single square, provided that the token stays on the strip. How many ways can the token … 
math
Two players play a game on the Cartesian plane. The game starts by placing a token at a lattice point in the first quadrant. The players alternate turns, with player one going first. On her turn, player 1 can move the token 2 units … 
probability
Betty has several of the standard sixsided dice that are common in many board games. If Betty rolls one of these dice, what is the probability that she rolls a three? 
Math
a trading token is in the shape of a trapezoid and has an area of 25 square centimeters and the bases are 3 and 7 centimeters what is the height of the token.