Question

Assume that there are 8 rats in the cage: 6 trained and 2 untrained. A rat is removed from the cage and it is noted whether or not it is trained. It is then placed in a different cage. 4 more rats are removed and treated the same way. How many outcomes are possible for this experiment?

Answer 1

The number of possible outcomes for the experiment is 64.

Step-by-step explanation:

In this experiment, there are 8 rats in the cage, with 6 trained and 2 untrained. First, one rat is removed from the cage and placed in a different cage, noting whether it is trained or not. Then, four more rats are removed and treated in the same way. We need to determine the number of possible outcomes for this experiment.

Since there are two possible outcomes for each rat (trained or untrained), and the trials are independent and conducted under identical conditions, we can multiply the number of outcomes for each rat. Therefore, the total number of outcomes for this experiment is 25 * 2 = 64.

Answer 2

First remove:

Probability of removing a trained rat is 6/8

Probability of removing untrained rat is 2/8

Outcome is 6/8 + 2/8 = 1

Second remove:

Probability of picking a trained rat is 5/7

Probability of picking untrained rat is 1/7

Outcome is 6/7

Third remove:

Outcome is 1 (Since you can only remove a trained rat)

Forth remove:

Outcome is 1 (Since you can only remove a trained rat)

Fifth remove:

Outcome is 1 (Since you can only remove a trained rat)

Total outcome = 1 + 6/7 + 1 + 1 + 1 = 34/7 = 4(6/7)