Suppose that a fair, 6 sided die is rolled. Let X indicate the event that an even number is rolled (in other words, X = 1 if an even number is rolled and X = 0 otherwise). Let Y indicate the event that 2, 3, or 4 is rolled (in other words, Y = 1 if 2, 3, or 4 is rolled and Y = 0 otherwise). Find P (X = 0, Y = 1).

1/2, 1/2

Step-by-step explanation:

A die has 6 faces.

Total number of faces = 6

Possible outcomes are :1,2,3,4,5,6

Even numbers : 2, 4, and 6 = 3

Non even numbers: 1,3,and 5= 3

First statement:

P(Even number) = 3/ 6 = 1/2

P(X=1) = 1/2

P(odd number) = 3/6 = 1/2

P(X=0) = 1/2

Second statement:

P(2) = 1/6

P(3) = 1/6

P(4) = 1/6

P(2 or 3 or 4) = (1/6) + (1/6) + (1/6)

P(2 or 3 or 4) = (1+1+1)/6 = 3/6 =1/2

Thus,

P(Y=1) = 1/2

Therefore,

P(X =0,Y=1) = 1/2, 1/2

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

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