Question

A learning experiment requires a rat to run a maze (a network of pathways) until it locates one of three possible exits. Exit 1 presents a reward of food, but exits 2 and 3 do not. (If the rat eventually selects exit 1 almost every time, learning may have taken place.) Let Yi denote the number of times exit i is chosen in successive runnings. For the following, assume that the rat chooses an exit at random on each run.

Required:
Find the probability that n = 6 runs result in Y1=3,Y2=1, and Y3=2

Answer 1

Find the probability that n = 6 runs result in Y1=3,Y2=1, and Y3=2

=0.823

Explanation:

Multinomial distribution

p(y1;y2,y3…..yk) = (n!/y1!,y2!,y3!…y4!) x p1^y1 x p2^y2 x p3^y3 x pk^yk)

The rat chooses of the three exists at random:

p = 1/3

p(3,2,1) = 6! / 3! 1! 2! (1/3)^3 (1/3)^1 (1/3)^2

=20/243

=0.823