An urn contains 11 balls, 3 white, 3 red, and 5 blue balls. Take out two balls at random, without replacement. You win $1 for each red ball you select and lose a $1 for each white ball you select. Let X be the random variable that notes the amount you win. Find the probability mass function (p. m.f.) of X.

Given: An urn contains 11 balls, 3 white, 3 red, and 5 blue balls.

You win $1 for each red ball you select and lose a $1 for each white ball you select.

Let X be the number of times you win.

The total number of ways to select 2 balls (order does not matter) =

The number of ways so that two balls are white (and

The number of ways so that two balls are red (and

The number of ways so that one ball is red, one is white (and

The number of ways so that two balls are blue (and ):

i.e.

The number of ways so that one ball is blue, one is white (and ):

The number of ways so that one ball is blue, one is red (and ):

Thus, the probability mass function (p.m.f.) of X would be ( in attachment) :

i will pick c put check it over to be sure

step-by-step explanation:

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.