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iris [78.8K]
3 years ago
13

PLEASE I NEED YOUR HELP ​

Mathematics
2 answers:
gladu [14]3 years ago
5 0

Answer:

-(7/9)

Step-by-step explanation:

Tcecarenko [31]3 years ago
4 0

Answer:

<h2>D) - 9/7</h2>

Hope this will help you lot.

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A bag contains two six-sided dice: one red, one green. The red die has faces numbered 1, 2, 3, 4, 5, and 6. The green die has fa
gayaneshka [121]

Answer:

the probability the die chosen was green is 0.9

Step-by-step explanation:

Given that:

A bag contains two six-sided dice: one red, one green.

The red die has faces numbered 1, 2, 3, 4, 5, and 6.

The green die has faces numbered 1, 2, 3, 4, 4, and 4.

From above, the probability of obtaining 4 in a single throw of a fair die is:

P (4  | red dice) = \dfrac{1}{6}

P (4 | green dice) = \dfrac{3}{6} =\dfrac{1}{2}

A die is selected at random and rolled four times.

As the die is selected randomly; the probability of the first die must be equal to the probability of the second die = \dfrac{1}{2}

The probability of two 1's and two 4's in the first dice can be calculated as:

= \begin {pmatrix}  \left \begin{array}{c}4\\2\\ \end{array} \right  \end {pmatrix} \times  \begin {pmatrix} \dfrac{1}{6}  \end {pmatrix}  ^4

= \dfrac{4!}{2!(4-2)!} ( \dfrac{1}{6})^4

= \dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^4

= 6 \times ( \dfrac{1}{6})^4

= (\dfrac{1}{6})^3

= \dfrac{1}{216}

The probability of two 1's and two 4's in the second  dice can be calculated as:

= \begin {pmatrix}  \left \begin{array}{c}4\\2\\ \end{array} \right  \end {pmatrix} \times  \begin {pmatrix} \dfrac{1}{6}  \end {pmatrix}  ^2  \times  \begin {pmatrix} \dfrac{3}{6}  \end {pmatrix}  ^2

= \dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^2 \times  ( \dfrac{3}{6})^2

= 6 \times ( \dfrac{1}{6})^2 \times  ( \dfrac{3}{6})^2

= ( \dfrac{1}{6}) \times  ( \dfrac{3}{6})^2

= \dfrac{9}{216}

∴

The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )

The probability of two 1's and two 4's in both die = \dfrac{1}{216} \times \dfrac{1}{2} + \dfrac{9}{216} \times \dfrac{1}{2}

The probability of two 1's and two 4's in both die = \dfrac{1}{432}  + \dfrac{1}{48}

The probability of two 1's and two 4's in both die = \dfrac{5}{216}

By applying  Bayes Theorem; the probability that the die was green can be calculated as:

P(second die (green) | two 1's and two 4's )  = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)

P(second die (green) | two 1's and two 4's )  = \dfrac{\dfrac{1}{2} \times \dfrac{9}{216}}{\dfrac{5}{216}}

P(second die (green) | two 1's and two 4's )  = \dfrac{0.5 \times 0.04166666667}{0.02314814815}

P(second die (green) | two 1's and two 4's )  = 0.9

Thus; the probability the die chosen was green is 0.9

8 0
3 years ago
The sum of 4 consecutive integers is 198. What is the fourth number in this sequence.
Georgia [21]
Let x, x+1,x+2, x +3 are the <span>numbers
so
</span>x + x +1 + x +2 +x +3 = 198
4x + 6 = 198
4x =198-6
4x = 192
 x = 192/4
 x = 48
 x + 1 = 48 + 1 = 49
 x + 2 = 48 + 2 = 50
 x + 3 = 48 + 3 = 51

proof
48 + 49 + 50 + 51 = 198

so the numbers are 48, 49, 50, 51

fourth number in this sequence is 51
7 0
3 years ago
Describe what each transformation does to pre image to create its image
Kamila [148]
A rotation rotates the pre image an x amount of degrees
a translation shifts a pre image up and down or left and right
a reflection reflects an image across an x or
y axis
a dilation stretches or compresses(shrinks) a pre image
7 0
3 years ago
Explain in a minimum of 2 sentences how to graph the equation of the absolute value function given a vertex of (-1,3) and a valu
VladimirAG [237]
This would be y = |x+1| + 3
7 0
3 years ago
Determine the perimeter of the triangle.<br> 3x<br> x + 6<br> 5x – 7
Gekata [30.6K]

Answer:

9x-1

Step-by-step explanation:

The perimeter of the triangle is adding up all 3 sides.

(3x)+(x+6)+(5x-7)=P

9x-1 = perimeter

All I have done is combine like terms.

If there is a... x = something, replace x with the number.

8 0
3 years ago
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