I need help with math

A lab animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one food on one trial,

Tresset [83]

Answer:

The probability that it will choose food #2 on the second trial after the initial trial = 0.3125

Step-by-step explanation:

Given - A lab animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one food on one trial, it will choose the same food on the next trial with a probability of 50%, and it will choose the other foods on the next trial with equal probabilities of 25%.

To find - If the animal chooses food #1 on an initial trial, what is the probability that it will choose food #2 on the second trial after the initial trial?

Proof -

By the given information, we get the stohastic matrix

$H = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]$

As we know that,

The matrix is a Markov chain $x_{k+1} = Hx_{k}$

Let

The initial state vector be

$x_{0} = \left[\begin{array}{ccc}1\\0\\0\end{array}\right]$

we choose this initial vector because given that If the animal chooses food #1 on an initial trial.

Now,

$x_{1} = Hx_{0} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}1\\0\\0\end{array}\right] \\= \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right]$

∴ we get

$x_{1} = \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right]$

Now,

$x_{2} = Hx_{1} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right] \\= \left[\begin{array}{ccc}0.25+0.0625+0.0625\\0.125+0.125+0.0625\\0.125+0.0625+0.125\end{array}\right]\\= \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right]$

∴ we get

$x_{2} = \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right]$

∴ we get

The probability that it will choose food #2 on the second trial after the initial trial = 0.3125

4 0

3 years ago

You want to decorate your wording studio with famous record album covers. The rectangular region you want to decorate measures 7

GarryVolchara [31]

Answer:

First find the area 72*63

A=4536

Then find the area 12*12

A=144

Then divide 4536/144

You would need 31.5 12 by 12in covers to decorate the rectangular region

As for the 6 by 6

You would need 126 album covers

As for the 9 by 9

You would need 51 covers

And as for the 15 by 15

You would need 20.6 covers

4 0

4 years ago

Scarlett has set up a lemonade stand outside her house and sells small cups

r-ruslan [8.4K]

Answer: Scarlett sold 40 small cups and 30 large cups

8 0

4 years ago

Data for the estimated number of HIV cases worldwide between 1988 and 1996 suggests exponential growth in the number of cases ov

Eduardwww [97]

Answer:

d. 52.5 million cases

Step-by-step explanation:

from the data output in the question, we have the regression equation to be

log y = -151.281 + 0.076577x

y is the number of hiv cases which is in millions

x is the year of the hiv case

x = 1998

we put the value of x in the regression equation

log y = -151.281 + 0.076577(1998)

log y = -151.281 + 153.000846

log y = 1.719846

since the result is in log form,

$y=10^{1.791846}$

y = 52.5 million cases

3 0

3 years ago

What is 44/7 converted into a mixed number

Cerrena [4.2K]

the answer to your equation is 42 2/7

6 0

3 years ago