If P(x) = 0.20, find the complement.

A six-sided die is rolled two times. What is the theoretical fractional probability that the first number is greater than the se

Alekssandra [29.7K]

Given:

A six-sided die is rolled two times.

To find:

The theoretical fractional probability that the first number is greater than the second number.

Solution:

If a six-sided die is rolled two times, then the total possible outcomes are 36.

S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

The outcomes where the first number is greater than the second number are

A = {(2,1), (3,1), (3,2), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (5,4), (6,1), (6,2), (6,3), (6,4), (6,5)}

So, the favorable outcomes = 15.

Now, the theoretical fractional probability that the first number is greater than the second number is

$Probability=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

$Probability=\dfrac{15}{36}$

$Probability=\dfrac{5}{12}$

Therefore, the required probability is $\dfrac{5}{12}$ .

5 0

3 years ago

PLEASE HELP I'M ON A TIMER! thanks

Zepler [3.9K]

Oh i done this yes sir u r correct

8 0

4 years ago

A game you want is on sale for 15% off.if the regular price is $50.00,how much will you save?and what will the total sale price

olganol [36]

Answer:

you will save 7.50$ and the total sale will be 42.50

Step-by-step explanation:

7 0

3 years ago

10. Given matrices A, B, and C below, perform the indicated operations if possible. If the operation is not possible, explain wh

Artemon [7]

Answer(a):

Order of matrix A = 3x3 {because number of rows=3, number of columns=3}

Order of matrix B = 3x3

Order of matrix C = 1x3

3A will be of order 3x3 because multiply by scalar doesn't change the order. Which is same as the order of matrix B.

So 3A+B is possible.

We simply multiply all elements of A with 3 and add them with corresponding elements of B.

$3\begin{bmatrix}2 & -1& 0\\ 0 & 5& 0.3\\ 1 & 4&10 \end{bmatrix}+\begin{bmatrix}5 & 0& 2\\ 1 & -3& 9\\ 2 & 0& 4\end{bmatrix}= \begin{bmatrix}11 & -3& 2\\ 1 & 12& 9.9\\ 5 & 12& 34\end{bmatrix}$

Answer(b):

2B will be of order 3x3 because multiply by scalar doesn't change the order. Which is NOT same as the order of matrix C.

So 2B+C is NOT possible.

Answer(c):

CA is possible only if

number of columns of C = number of columns of A

3=3

which is true hence CA is possible.

$\begin{bmatrix}1 &3 &5 \end{bmatrix}*\begin{bmatrix}2 & -1& 0\\ 0 & 5& 0.3\\ 1 & 4&10 \end{bmatrix}=\begin{bmatrix}1*2+3*0+5*1 & 1*-1+3*5+5*4 & 1*0+3*0.3+5*10\end{bmatrix}$

= $\begin{bmatrix}7 & 34& 50.9\end{bmatrix}$

<em><u>If the matrix is not visible properly then look at the attached picture.</u></em>

5 0

3 years ago

3. Write 0.46 as a fraction.

Anika [276]

Answer:

so 0.46 is equal to 414/900

4 0

2 years ago