Question

According to Webster’s New Collegiate Dictionary, a divining rod is "a forked rod believed to indicate [divine] the presence of water or minerals by dipping downward when held over a vein." To test the claims of a divining rod expert, skeptics bury four cans in the ground, two empty and two filled with water. The expert is led to the four cans and told that two contain water. He uses the divining rod to test each of the four cans and decide which two contain water. a List the sample space for this experiment. b If the divining rod is completely useless for locating water, what is the probability that the expert will correctly identify (by guessing) both of the cans containing water?

Answer 1

1/6

Explanation:

Let E1 and E2 represent the empty cans and W1 and W2 be the cans filled with water.

S = { E1E2, E1W2,E2W2, E1W1, E2W1, W1W2 }

By merely guessing, the events are equally likely. Since there are 6 possible outcomes,

probability = 1/6