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Rzqust [24]
3 years ago
7

The probability of winning a particular game at the Game Place is 14 1/4 . Find the odds against winning the game.

Mathematics
1 answer:
Zinaida [17]3 years ago
6 0
ANSWER

\frac{1}{3}



EXPLANATION

We want to find an odds ratio from a given probability, which is


\frac{1}{4}


We subtract the numerator 1 from the denominator 4 to obtain


4- 1= 3


The answer is the number of unfavorable outcomes. 

The Odds can then be expressed as

1 : 3


The ratio of favourable outcomes to unfavorable outcomes.


Or

\frac{1}{3}




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Answer:

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Step-by-step explanation:

Given that

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We know that:

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Comparing (1) and (2)

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Using power series expansion for tan^{-1}x

f'(x)=-tan^{-1}x=-\int {\frac{1}{1+x^{2}} \, dx

= -\int{ \sum\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx

= -\sum{ \int\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx

=-[c+\sum\limits^{ \infty}_{n=0} (-1)^{n}\frac{x^{2n+1}}{2n+1}]

=C+\sum\limits^{ \infty}_{n=0} (-1)^{n+1}\frac{x^{2n+1}}{2n+1}

=C-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....

as

                 tan^{-1}(0)=0 \implies C=0

Hence,

\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....

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