Bob spends the majority of a certain evening in his favorite drinking establishm
ID: 3182935 • Letter: B
Question
Bob spends the majority of a certain evening in his favorite drinking establishment. Eventually, he decides to spend the rest of the night at the house of one of his two friends, each of whom lives ten blocks away in opposite directions. However, being a bit intoxicated, he engages in a so-called “random walk” of n = 10 blocks where, at the start of each block, he first either turns and faces due west with probability 0.6, or independently, turns and faces due east with probability 0.4, before continuing. Using this information, answer the following. Hint: Let the discrete random variable X = “number of east turns in n = 10 blocks.” (0, 1, 2, 3, …, 10)
(d) How far, and in which direction, from where he started is he expected to end up, on average? (Hint: Combine the expected number of east and west turns.)
(e) With what probability does this occur?
Explanation / Answer
On on average, he is expected to walk 6 steps west(10*0.6) and 4 steps east(10*0.4). In all, he is expected to end 2 steps to the west.
Probability of this occuring = 10C6 * 0.6^6 0.4^4 = 0.69