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Milani's teacher draws students names at random, calls on the student, and replaces the name so that students know they should always be prepared to respond. There are \[20\] students in Milani's class. Let \[X\] be the number of names it takes for the teacher to draw Milani's name. Find the probability that the teacher first draws Milani's name as the \[7^{\text{th}}\] name. You may round your answer to the nearest hundredth. \[P(X=7)=\]

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Answer:

Step-by-step explanation:

For 1 call:

P(Milani's name is not called ) = 19/20

P(Milanis name is called) = 1/20.

For the first 6 calls her name is not called.

P(first 6, name not called)  = (19/20)^6

On the 7th call Milani is picked, so

P(X = 7) =  (19/20)^6 * 1//20

= 0.03675459

= 0.04 to the nearest hundredth.

NOTE: The individual probabilities are multiplied because each call is independent.