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A farmer from Whidbey Island: A man claims his whalebone can detect water. You design an experiment using a set of 4 cans, 3 empty, and one filled with water. You present the farmer with a total of 5 different but similar sets of cans. For each trial, you ask the farmer to identify which of the four cans has the water. How many cans would you expect the farmer to correctly identify by chance? (Round to the nearest 4 decimal places.)

Answer :

okpalawalter8

Answer:

The value is [tex]E(x) = 1.25 [/tex]

Step-by-step explanation:

From the question we are told that

The number of cans is n = 4

The number of can that are empty is N = 3

The number of can filled with water is k = 1

The number number of sets of cans is w = 5

Generally probability of detecting the correct can is mathematically represented as

[tex]p = \frac{k}{n}[/tex]

=> [tex]p = \frac{1}{4}[/tex]

=> [tex]p = 0.25[/tex]

Generally probability of not detecting the correct can is mathematically represented as

[tex]q = 1- p[/tex]

[tex]q = 1- 0.25[/tex]

[tex]q = 0.75[/tex]

Generally the number of cans expected of the farmer to correctly identify by chance is mathematically represented as

[tex]E(x) = w * p[/tex]

=> [tex]E(x) = 5 * 0.75 [/tex]

=> [tex]E(x) = 1.25 [/tex]

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