A pair of fair dice is cast. Let Edenote the event that the number landing uppermost on the first die is a 1 and let Fdenote the event that the sum of the numbers falling uppermost is 5. Determine whether Eand Fare independent events. Show your calculationsby describing the sample space, theeventsE and F, and combinations of these events as needed.

They are not independent

Step-by-step explanation:

Given

E = Occurrence of 1 on first die

F = Sum of the uppermost occurrence in both die is 5

Required

Are E and F independent

First, we need to list the sample space of a roll of a die

Next, we list out the sample space of F

In (1): the sample space of E is:

So:

In (2): the sample space of F is:

So:

For E and F to be independent:

Substitute values for P(E) and P(F)

This gives:

However, the actual value of P(E and F) is 0.

This is so because and have 0 common elements:

So:

Compare and .

These values are not equal.

Hence: the two events are not independent

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

37

step-by-step explanation: