Exercise 4.4. Liz is standing on the real number line at position O. She rolls a die repeatedly. If the roll is 1 or 2, she takes one step to the right (in the positive direction). If the roll is 3, 4, 5 or 6, she takes two steps to the right. Let Xn be Liz's position after n flips of the coin. Estimate the probability that x90 is at least 160.

Probability that is at least 160 is 0.0127

Step-by-step explanation:

Probability that is at least 160

Probability that she rolls 1 or 2 i.e. probability that she takes one step to the right:

P(X=1) = 2/6 = 1/3

Probability that she rolls 3,4,5,6 i.e. Probability that she takes two steps to the right:

P(X=2) = 4/6 = 2/3

when x = 1,2

The mean value after n flips

For the standard deviation:

Where Z =

= 0.9873

only 10/60 isn't equivalent

hope this : )