Question

A comparative psychologist wants to know if cats have color vision. She trains cats to press a green button to obtain a food reward. She then gives the cats a choice between pressing a green button, a red button, a blue button, and a black button but only rewards the cat with food when it presses the green button. The study involves testing each cat on 18 different trials. The position of the 4 colored buttons are randomized across the 18 trials. Assume that the cats cannot distinguish between the green, red, blue, black buttons.

Question: What is the most probable number of trials out of 18 that will result in the cat pressing the green button? What is the probability of the cat pressing the green button on this number of trials out of 18.

Answer 1

Mean number of trials in which cat press the green button = np = 18*0.25 = 4.5

Thus, the most probable number can be either 4 or 5

Now, P(X = 4) = = 0.213

P(X = 5) = = 0.199

Thus the most probable number of trials out of 18 that will result in the cat pressing the green button is 4

The corresponding probability is 0.213