Sophia_xx
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A game is played with a token on a board with a grid printed on it. The token starts at the point (0, 0) and moves in steps. Each step is either 1 unit in the positive x-direction with probability 0.8, or 1 unit in the positive y-direction with probability 0.2. The token stops when it reaches a point with a y-coordinate of 1. It is given that the token stops at (X, 1).
(i) (a) Find the probability that X = 10.
(b) Find the probability that X < 10.
(ii) Find the expected number of steps taken by the token.
(iii) Hence, write down the value of E( X ).

I dont understand the question or how to work out any of the solutions please can somebody help me ? !

I especially dont understand part b)
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TSR Jessica
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Sorry you've not had any responses about this. Are you sure you’ve posted in the right place? Posting in the specific Study Help forum should help get responses.

I'm going to quote in Puddles the Monkey now so she can move your thread to the right place if it's needed. :yy:

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buckeybarnes
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It's only guesswork because I'm not a stats prodigy or anything lol

ia. i would expect this to be 0.8^10 or smth? because it must move in the x-direction 10 times before it moves in the y-direction, so I would expect something reminiscent of a geometric distribution with Geo(0.8) idk?
b. unsure, but it would mean that the counter had moved in the y-direction before 10 moves in the x-direction had occurred, the only way i could process this is to add all of x=0,1,2,3,4,5,6,7,8,9 together, idk if that'd take too long it'd be like- (0.2)+(0.2x0.8)+(0.2x0.8^2)... etc until (0.2x0.8^9) i think idk
ii. expected number of steps i would guess would just be 8? because you have an 8/10 chance of going in the x-direction until you are expected to roll a y and stop.
iii. idk sorry its a weird af question

please dont take this as the answer this is just guesswork, is there a mark scheme hidden anywhere? would be good if we could read it and see the real answers
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buckeybarnes
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wait im wrong sorry that mark scheme makes no sense tho tough paper
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buckeybarnes
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only needed 75% 54/72 for an A thought i guess thats a bit reassuring lol
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micycle
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ai) 0.8^10*0.2 = 0.0215
bi) What buckey suggested, or use sum to n of a geometric series with a= 0.2, r= 0.8, n=10. (=0.8926)
bii) We stop when we get a y. This assuredly will happen after 0.2^-1 = 5 attempts.
biii) We land on 0.2 on the fifth go so this is the final step. Therefore beforehand we covered 4 X units, so = 4.

These could be wrong.
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