A farmer came to the Water Resources Laboratory of the University of waterloo. T

Question

A farmer came to the Water Resources Laboratory of the University of waterloo. The farmer brought a carved whalebone with which he claimed that he could locate hidden sources of water. The following experiment was conducted to test the farmer's claim. He was taken into a room in which there were 10 covered cans. He was told that 5 of the 10 cans contained water and 5 were empty. The farmer's task was to divide the cans into two equal groups, 1 group containing all the cans with water, the other containing those without water. What is the probability that the farmer correctly put at least 3 cans into the water group just by chance?

Explanation / Answer

Number of ways in which r items can be selected from n, nCr = n!/(r! x (n-r)!

P(farmer puts at least 3 can correctly) = P(3 correct and 2 incorrect) + P(4 correct and 1 incorrect) + P(5 correct)

= 5C3x5C2/10C5 + 5C4x5C1/10C5 + 5C5/10C5

= 10x10/252 + 5x5/252 + 1/252

= 0.4405

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