To test the claims of a diving rod expert, skeptics bury SIX cans in the ground,

Question

To test the claims of a diving rod expert, skeptics bury SIX cans in the ground, three empty and three filled with water. The expert is led to the SIX cans and told that three contain water. He uses the diving rod to test each of the SIX cans and decide which three contain water.

Suppose the diving rod is usless for locating water.

Find the probability that the expert will correctly identify:

a) all three of the cans containing water

b) At least two of the three cans contain water

For each can we have the following: Let W = water and E= Empty (x,y) where x is what the diver claims and y is the ctual observation.

(Wi,Ei), (Wi,Wi), (Ei, Wi), (Ei,Ei) for every i from 1 to 6.

I'm just getting stuck/confused where to go with this..

Explanation / Answer

a) No of ways of chossing thre cans out of 6 cans= 6C3= 20

No of ways in which he will correctly identify all thre cans of water=1

Probability=1/ 20= 0.05

b) Atleast two of the three cans

There are two cases

Case 1. Choose 2 correcr water cans

3C2* 3C1 ie 2 water cans out of three water cans and 1 empty can out of three empty cans are selectrd

Probability= 3*3. / Total ways of choosing any 3 cans

9/ 20

Case 2:

Choosing all three cans of water correctly= 0.05

Adding both the cases will give total probability=

0.05+ 0.45=0.5

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