2015 regional secondary no. 2 probability
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There are 9 seats for passengers in a water bus. Probability of ticket buyer of the water bus remains absent on the day of journey is 50%. If the owners of the water bus sell 11 tickets then the probability of every passenger getting a seat is a/b,where a and b are co-prime. b-a = ?
- Thanic Nur Samin
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- Joined:Sun Dec 01, 2013 11:02 am
Re: 2015 regional secondary no. 2 probability
The only cases where every passenger doesn't get a seat are when $10$ and $11$ passenger comes. The probability of these happening are simultaneously $\dfrac{11}{2^{10}}$ and $\dfrac{1}{2^{11}}$
So, the probability of everyone getting a seat would be $1-\dfrac{11}{2^{10}}-\dfrac{1}{2^{11}}=\dfrac{2^{11}-23}{2^{11}}$. So the answer is clearly $\boxed{23}$
So, the probability of everyone getting a seat would be $1-\dfrac{11}{2^{10}}-\dfrac{1}{2^{11}}=\dfrac{2^{11}-23}{2^{11}}$. So the answer is clearly $\boxed{23}$
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Because destroying everything mindlessly isn't cool enough.
- ahmedittihad
- Posts:181
- Joined:Mon Mar 28, 2016 6:21 pm
Re: 2015 regional secondary no. 2 probability
Erm, I'm getting a different result. The probability of $10$ passengers coming is $11/2^{11}$. The probability of $11$ passengers coming is $1/2^{11}$.
So the probability of everyone getting a seat would be $1- 11/2^{11} - 1/2^{11}=( 2^{11}-12)/2^{11}$. So the answer is $3$.
So the probability of everyone getting a seat would be $1- 11/2^{11} - 1/2^{11}=( 2^{11}-12)/2^{11}$. So the answer is $3$.
Frankly, my dear, I don't give a damn.
- Thanic Nur Samin
- Posts:176
- Joined:Sun Dec 01, 2013 11:02 am
Re: 2015 regional secondary no. 2 probability
Such a silly mistake by me. I guess this is what happens when you solve divisional problems after midnight without teaahmedittihad wrote:Erm, I'm getting a different result. The probability of $10$ passengers coming is $11/2^{11}$.
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Because destroying everything mindlessly isn't cool enough.