Well I don't know.
Let's think about it:

-- There are 6 possibilities for each role.
So 36 possibilities for 2 rolls.
Doesn't take us anywhere.

New direction:
-- If the first roll is odd, then you need another odd on the second one.
-- If the first roll is even, then you need another even on the second one.
This may be the key, right here !

-- The die has 3 odds and 3 evens.

-- Probability of an odd followed by another odd = (1/2) x (1/2) = 1/4
-- Probability of an even followed by another even = (1/2) x (1/2) = 1/4

I'm sure this is it. I'm a little shaky on how to combine those 2 probs.

Ah hah !
Try this:

Probability of either 1 sequence or the other one is (1/4) + (1/4) = 1/2 .

That means ... Regardless of what the first roll is, the probability of
the second roll matching it in oddness or evenness is 1/2 .

So the probability of 2 rolls that sum to an even number is 1/2 = 50% .

Is this reasonable, or sleazy ?

4 0

3 years ago

A bag contains 63 marbles, some red and some green. The ratio of red marbles to green

Nikolay [14]

Answer:

45 green marbles

Step-by-step explanation:

6 0

2 years ago

"A rectangle has a height of 5 cm and its base is increasing at a rate" of 3/2 cm/min. When its area is 60 cm2, at what rate is

sukhopar [10]

Answer:

The diagonal is increasing at the rate of 119/104cm/min of the given rectangle.

Step-by-step explanation:

Dimensions of the rectangle

Height = 5cm

Rate of base = 3/2 cm/min

Area = 60cm^2

We know the area of a rectangle of given by = base* Height

b*h = 60

b*5 = 60

b = 12cm

Applying Pythagoras theorem while drawing a diagonal to the rectangle

$b^2 +h^2 = D^2\\$

$5^2 +12^2 = 13^2$

so our diagonal will be 13cm

Upon differentiating the area of the rectangle we get

b*h = A=60cm^2

using the chain rule of differentiation

h*db/dt + b*dh/dt = 0

b*dh/dt = -h*db/dt

12*dh/dt = -5*3/2

dh/dt = -5/8 cm//min

so the height of the rectangle is decreasing at the rate of -5/8cm/min

now we have all the measurements we need

b = 12 , db/dt = 3/2cm/min

h = 5 , dh/dt = -5/8 cm/min

$b^2 +h^2 = D^2$

Upon differentiating we get

2b*db/dt + 2h*dh/dt = 2D*dD/dt

b*db/dt + h*dh/dt = D*dD/dt

12*3/2 + 5*(-5/8) = 13*dD/dt

18 -25/8 = 13*dD/dt

$\frac{144-25}{8}$ = 13*dD/dt

dD/dt = $\frac{119}{104} cm/min$

Therefore the diagonal is increasing at the rate of 119/104cm/min of the given rectangle.

6 0

3 years ago