Every time it moves, this robot either hops exactly one dot to the left or one dot to the right. If the robot starts in the center of this pattern, what is the probability that, after four hops, it's positioned on top of a blue dot? A. 1/2 B. 1/3 C. 1/4 D. 2/9
@brilliantorg Is in the middle position of the not blue and blue so is 1/2
@brilliantorg Let’s say if it moves forward then it is +1 and if it moves backward it’s -1. Total number of permutations for 4 moves =16. Out of which sum should be either +2 or -2. will be (-1-1-1+1) —> (4!/3!) = 4 (-2) & (-1+1+1+1) —> (4!/3!) = 4 (+2). Prob = (4+4)/16=1/2
@brilliantorg On just a blue dot, it’s 1/2. On the left or right blue dot it’s 1/4.
@brilliantorg Since we are given 4 moves, we can simulate all the possible options which are in total 2^4 = 16. For each next move, there is a 50-50 chance for going right or left. From the image, (4+4)/16 = 1/2
@brilliantorg @brilliantorg when are the next problems coming at Twitter?