1. ## Question

If anyone can help me with any of these three problems, Its 2 am where I am at.. n I cant sleep until these are finished, i tried looking in my book to further explain, but I am totally stuck any help would be so greatly appreciated... Thank u so much:

41. What is the probability of rolling a nine
with a pair of dice consecutively followed
by rolling a five with a pair of dice?
Hint: Consecutive events are products of
individual probabilities.

57. Find the 5th term of the binomial expansion.

(2x-3y)^7

58. Identify and sketch the graph for the
relation:

y^2 +x^2 – 6x + 9 = 25
Hint: Make a table, let xmin be -2 and xmax be 8, Move all the monomials over to the right hand side except y^2 , then solve for the two values of y when taking the square root, note the positive and negative cases. After making a table, plot the points on graph paper and identify the shape.

2. For the probability of two dice summing to nine, you can have:

$3 + 6,\,\, 4 +5,\,\, 5 + 4,\,\, 6 + 3$

Each outcome has $P = \frac{1}{6}\,$, as the dice are fair.

So the probability is $4\, \left( \frac{1}{6} \times \frac{1}{6} \right) = \frac{1}{9}$

For the probability of two dice summing to five, you can have:

$1 + 4,\,\, 2 +3,\,\, 3 + 2,\,\, 4 + 1$

Which gives the same probability as for the sum of the dice to 9.
Because dice rolls are independent, the probability of rolling a 9 with 2 die followed by rolling 5 with 2 die $= \left(\frac{1}{9}\right)^2$

For binomial expansions,
The 5th term will be $_{\,}^7C_4 \,(2x)^3 \,(-3y)^4$ (binomial expansion formula).

3. For the last question,

$y^2 + x^2 - 6x + 9 = 25$

You need to complete the square for x (the y term is already a perfect square)

$y^2 + (x - 3)^2 = 25$

Now this is the standard equation for a circle. The centre will be at $(3,0)$, and the radius is $\sqrt{25} = 5$

To sketch this, place the compass point at $(3,0)$ and draw a circle of radius 5 units.

4. Originally Posted by Steph07
What is the probability of rolling a nine
with a pair of dice consecutively followed
by rolling a five with a pair of dice?
Hint: Consecutive events are products of
individual probabilities.
Pr(rolling a 9) x Pr(rolling a 5).

Use this dice table to help calculate each probability: Dice table