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March 12th, 2016, 03:48 PM   #1
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Basic Stats Problem!

Hey all -

Going through an intro to stats class here, and am having an issue with a homework problem that we have not covered in class yet. Here it is:

“As a poor college student, I bought four $2 scratchers in hopes to win some extra cash. On the back of the scratcher, it said the odds of winning are 1 out of every 3.8. So with my quick thinking I thought I would for sure win. I scratched all of them and didn't win anything. What is the likelihood of that happening?”

I know the reason why he didn't win, but I am looking for some help with the probability numbers itself of him not winning after scratching 4 of them (at a 1 in 3.8 chance)

I am sure the answer is trivial and simple, but I am stuck.

Really appreciate the help!

Last edited by snewman2; March 12th, 2016 at 03:51 PM.
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March 12th, 2016, 05:31 PM   #2
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The probability of him winning on one of the scratchies is $\dfrac{1}{3.8} = \dfrac{5}{19}$.
Thus, the probability of him losing on one of the scratchies is $1 - \dfrac{5}{19} = \dfrac{14}{19}$.

Since he lost on all four scratchies, the required probability is $\left(\dfrac{14}{19}\right)^4$.
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March 12th, 2016, 05:47 PM   #3
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Quote:
Originally Posted by Azzajazz View Post
The probability of him winning on one of the scratchies is $\dfrac{1}{3.8} = \dfrac{5}{19}$.
Thus, the probability of him losing on one of the scratchies is $1 - \dfrac{5}{19} = \dfrac{14}{19}$.

Since he lost on all four scratchies, the required probability is $\left(\dfrac{14}{19}\right)^4$.
You are a god sir. Thanks for the quick reply. I completely understand that concept now, and it will really help me going forward.

Appreciate it!
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