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probabilty !!

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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probabilty !!

by marmar29 » Sat Apr 16, 2011 12:50 am
The diagram shows a spinner with six numbered sections.(where it has number 2 twice, # 1 triple & # 6 once )
Some of the sections are shaded.
Each time the spinner is spun it stops on one of the six sections.
It is equally likely that it stops on any one of the sections.

the question is :
The spinner is now spun until it stops on a section numbered 2.
The probability that this happens on the nth spin is
16243
.
Find the value of n.
kindlty show the steps
eager to see the solution
marmar
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by therealtomrose » Sat Apr 16, 2011 6:05 am
Marmar, either you left something out, or that is not an official GMAT problem from the OG. Here is a method that you can use for calculating the probability of hitting a 2 on the nth spin.

First calculate two simple probabilities:
Probability (lands on space labeled 2) = (success cases) / (possible cases) = (2) / (6) = 1/3
Probability (lands on space NOT labeled 2) = (success cases) / (possible cases) = (4) / (6) = 2/3

You want to know the probability that you will land on a 2 on the nth spin. 'n' in this case is not something you solve for. 'n' is something you plug in before looking for a probability. For example:

The probability you will hit 2 on the first spin (n=1) is 1/3 (see above for calculation)

The probability you will hit 2 (for the first time) on the second spin (n=2) is more complicated. You need to calculate the probability that you spin a non-2 on the first try, then a 2 on the second try. The probability of successive, independent events is calculated by multiplying the probability of each event together.
Probability (hitting a 2 for the 1st time on the 2nd spin) = Probability (lands on space NOT labeled 2) * Probability (lands on space labeled 2) = (2/3) * (1/3) = 2/9

You can generate a formula based on 'n' for the Probability (hitting a 2 for the first time on nth spin), but this is certainly outside the scope of the GMAT. Here is the formula (defined for whole number n's greater than 1.)
Probability (hitting a 2 for the first time on nth spin) = (1/3)^(n-1)*(2/3)

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