7 Counting and Probability Answer the following questions about counting and probability. You may leave answers in the form of exponents, fractions and factorials, but not combinations or permutations. Show your work. a) Consider rolling two fair 6-sided dice. What is the conditional probability that the sum of the two dice is at least 8 given the first dice is at most 4?

Q: Solve for x, y and z x + 2y - z = 0 2x + 3y - 2z = 3 -x - 4y + 3z = - 2

A: x+2y-z=0            i2x+3y-2y=3        ii-x-4y+3z=-2    iiii+iii-2y+2z=-2⇒-y+z=-1…

Q: x2 +4 y" + -y! ? y=x | x2

A:

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A:

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Q: (1+ ye" + xye")dæ + (xe² + 2)dy = 0 C = xye² + 2y+ x C = xye" – 2y – x %3D - Option 3 O Option 4 C =…

A: ANSWER: Option 3.

Q: 1. 5х2у" + 23ху' + 16.2у —D 0 2. х?у" + 0.7ху' — 0.1у %3D 0 3. х2у" — 0.7ху — 0.1у %3D0 |

A: Given

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A: Find value of x

Q: solve  w''' - 4w'' - 25w' + 100w = 0 how many linear independent solution to the equation needed…

A: solve  w''' - 4w'' - 25w' + 100w = 0 how many linear independent solution to the equation needed to…

Q: Solve for u. u/2 + 3u/4 = u/8

A:

Q: Would you mind explaining why sub part a is incorrect? And could you please explain the solution of…

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Q: Is -2 a solution to 30 = -5(6n + 6)?

A:

Q: A generator for a continuous time Markov process X(t) is given by G = 2 2 ー人 (1 0 a

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Q: is a solution of y"+ry 0 and write the

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Q: 5. Solve IVP у" - 4y" + 7y - бу %3D 0, у(0) %3D 1, у'(0) — 0, у" (0) — 0

A: See the attachment

Q: 52х + 67y + 46z %3D 175 67х + 73у + 54z %3D 194 46х + 54y + 65z %3D 165

A:

Q: 5. Solve the following PDE: b. 4 = a²u a²u əx² at²

A:

Q: The product of two whole numbers is 234 and their sum is 31. What are the two numbers?

A:

Q: 7. 2x-42 = 20 -3x + y- 42 = 20 -4x + 2y + 32 = -15

A: We will solve the following. As per the guidelines we can solve 1 problem only

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Q: v-102²³ 4. Solve Y for r.

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A: Consider a nth order differential equation dnydxn+dn-1ydxn-1+dn-2ydxn-2+.........................+y…

Q: 4. Simplify: (i – 1)² – (-i – 1)² + i*, i = v-1

A: Given: i-12--i-12+i4 ,  i=-1

Q: OS bisrets POR Salve for x and find mPOR. 16. mPOS- 3, mSOR- S-20

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A: To solve the equation.

Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

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A:

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.