Mathematics, 14.08.2020 18:01, ilovecatsomuchlolol

The Sorry State Lottery requires you to select five different numbers from 0 through 42. (Order is not important.) You are a Big Winner if the five numbers you select agree with those in the drawing, and you are a Small-Fry Winner if four of your five numbers agree with those in the drawing. (Enter your answers as exact answers.) What is the probability of being a Big Winner?

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answered: peytontanner

1 / 962598

Step-by-step explanation:

Let S be the sample space

total number of possible outcomes = n(S)

Let E be the event

total number of favorable outcomes = n(E)

Compute the number of ways to select 5 numbers from 0 through 42:

Total numbers to choose from = 43

Total number of ways to select 5 numbers from 43

= n(S) = 43C5

= 43! / 5! ( 43-5)!

= 43! / 5! 38!

= 43*42*41*40*39*38! / (5*4*3*2*1)*38!

= 115511760/120

n(S) = 962598

Hence there are 962598 ways to select 5 numbers from 43

Compute the probability of being a Big Winner

In order to be a Big Winner all 5 of the 5 winning balls are to be chosen and there is only one way you can for this event to occur. So

n(E) = 1

Here E is to be a Big Winner

So probability of being a Big Winner = P(E)

= n(E) / n(S)

= 1 / 962598

Hence

P(being a Big Winner) = P(E) = 1 / 962598

answered: Guest

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like, however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

$\bf e(\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad f(\stackrel{x_2}{0}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-2}{)}\implies \implies \cfrac{-2}{0+2}\implies \cfrac{-2}{2}\implies -1 \\\\[-0.35em] ~\dotfill$

$\bf d(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad f(\stackrel{x_2}{0}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{)}{)}\implies \cfrac{0+1}{0+2}\implies \cfrac{1}{2} \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope~of~ef}{-1\implies \cfrac{-1}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{1}{-1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{1}{1}\implies 1}}$