In a T-maze, a rate is given food if it turns left and an electric shock if it t

ID: 2983420 • Letter: I

Question

In a T-maze, a rate is given food if it turns left and an electric shock if it turns right. On the rst

trial there is a 50-50 chance that a rat will turn either way; then, if it receives food on a given trial

the probability that it will turn left on the next trial is 0.72, and if it receives a shock on a given trial

the probability that it will turn left on the next trial is 0.84.

1. What is the probability that the rat will turn left on the second trial?

2. Assuming the probability of a rat turning left on any given trials depends only on what it did

in the preceding trial, nd the probability that a rate will turn left on the third trial.

3. Removing the assumption in 2, calculate the expected number of trials that need to be made

until the rat turns right.

4. Removing the assumption from 2 again, calculate the expected number of trials needed until the

rat turns right two times in a row.

1) 0.5 * 0.72 + 0.5 * 0.84 = 0.78

2) since the probability for third trial will depend only on second trial...

0.5 * 0.72 + 0.5 * 0.84 = 0.78

3) the expected number of trials = 1/p = 1/0.5 = 2

4) the expected number of trials = 1/ (0.5)^2 = 4