Permutations + geometric progression (payout on a gambling machine)

Statistics008

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A gambling machine is programmed to pay out on 10% of the times that it is played. Whether or not the machine pays out on any throw is independent of the outcome on any other throw.

By using the formula for the sum of geometric progression(or otherwise) compute the probability that the machine pays out for the first time on an odd numbered throw.

A bag contains 5 balls which are number 1,2...,5. If balls are selected one at a time to form a five digit number, What is the probability that:

The number formed will be 12345?
The middle number will be a 3?

Help on these two questions will be greatly appreciated
 
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Subhotosh Khan

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A gambling machine is programmed to pay out on 10% of the times that it is played. Whether or not the machine pays out on any throw is independent of the outcome on any other throw.

By using the formula for the sum of geometric progression(or otherwise) compute the probability that the machine pays out for the first time on an odd numbered throw.

A bag contains 5 balls which are number 1,2...,5. If balls are selected one at a time to form a five digit number, What is the probability that:

The number formed will be 12345?
The middle number will be a 3?

Help on these two questions will be greatly appreciated
The number formed will be 12345? → Why not 54321?

What are your thoughts?

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Statistics008

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