When the health department tested private wells in a county for two impurities commonly found in drinking water, it found that 20% of the wells had neither impurity, 40% had impurity a, and 50% had impurity b. (obviously, some had both impurities.) if a well is randomly chosen from those in the county, find the probability distribution for y , the number of impurities found in the well.

P( Y = 0 ) = 0.2

P( Y = 1 ) = 0.7

P( Y = 2 ) = 0.1

Step-by-step explanation:

If 20% of wells didnt have impurities it could be said as that the probability that it didnt have A and didnt have B was 0.2:

P( not A ) ∩ P ( not B ) = 0.2

Also:

P( A ) = 0.4

P( B ) = 0.5

The formulas for the union of both impurities are:

P( A ) ∪ P( B ) = P( A ) + P ( B ) - P( A ) ∩ P ( B )

P( A ) ∪ P( B ) = 1 - P( not A ) ∩ P ( not B )

Replacing and solving you get:

P( A ) + P ( B ) - P( A ) ∩ P ( B )  = 1 - P( not A ) ∩ P ( not B )

0.4 + 0.5 - P( A ) ∩ P ( B ) = 1 - 0.2

P( A ) ∩ P ( B ) = 0.1

So the probability that the wells had both impurities is 0.1

P( A ) ∪ P( B ) = 0.8

This counts as having one of the impurities or both, in order to only have one impurity you need to substract when you have both:

one impurity = P( A ) ∪ P( B ) - P( A ) ∩ P ( B ) = 0.8 - 0.1 = 0.7

Now Y is the probabilty distribuion for the numbers of impuritis.

P( Y = 0 ) = 0.2 ( 0 impurities )

P( Y = 1 ) = 0.7 ( only 1 impurity )

P( Y = 2 ) = 0.1 ( 2 impurities )

idk

step-by-step explanation:

i don't know

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4