Chapter 15, Section 15.4, Exercise 1 Page 1,190

Step 1

A person has a chance of \(\frac{2}{3}\) shooting a ball.

P(shoot)= \(\frac{2}{3}\)

Chapter 15, Section 15.4, Exercise 2 Page 1,190

Step 1

The task is to find the probability that the basketball player made 1 out of 2 free throws if he is consistently making 2 out of 3 free throws. Also, in the exercise, we are given the solutions of Michael, Julie, and Erica and our task is to determine which is incorrect and which is correct.

Chapter 15, Section 15.4, Exercise 3 Page 1,192

Step 1

To get the probability of independent events, we multiply the probability of events A and B:

P(A and B)=P(A)⋅P(B)

A person shooting chance is \(\frac{2}{3}\) and not shooting the ball is \(\frac{1}{3}\)

P(shoot)=\(\frac{2}{3}\)

P(miss)=\(\frac{1}{3}\)

Chapter 15, Section 15.4, Exercise 4 Page 1,193

Step 1

The task is to find the probability that the basketball player will make 0,1,2, or 3 out of 3 free throws if he is consistently making 2 out of 3 free throws.

Chapter 15, Section 15.4, Exercise 5 Page 1,195

Step 1

The task is to calculate the probability that the player will make 0,1 and 2 out of 2 and 0,1 2, and out of free through using the combinations that determine in how many ways the required event can happen.

Chapter 15, Section 15.4, Exercise 6 Page 1,198

Step 1

The probability of independent events is equal to:

P(A and B)=P(A).P(B)

If there are multiply combinations of the events, we have:

⇒ \({ }_n C_r[P(A) \cdot P(B) \ldots]\)

A person has a shooting chance of \(\frac{2}{3}\) and missing chance of \(\frac{1}{3}\). Let us use the formulas above to solve the followin scenarios.

Chapter 15, Section 15.4, Exercise 7 Page 1,200

Step 1

The task is to complete the given table with a corresponding number of combinations that represent the number of ways a certain event can happen.

Chapter 15, Section 15.4, Exercise 8 Page 1,200

Step 1

Chapter 15, Section 15.4, Exercise 9 Page 1,201

Step 1

A person has a shooting chance of \(\frac{2}{3}\)
​, and the probability of missing is \(\frac{1}{3}\)

P(shoot)= \(\frac{2}{3}\)

P(miss)= \(\frac{2}{3}\)

Chapter 15, Section 15.4, Exercise 10 Page 1,202

Step 1

A person has a shooting of 2 out of 5 chance, and the probability of missing is \(\frac{3}{5}\)

P(shoot)= \(\frac{2}{5}\)

P(miss)= \(\frac{3}{5}\)

To get the probability of shooting r times in n shoots, we came up with the formula:

⇒ \({ }_n C_r \cdot[P(\text { shoot })]^r \cdot[P(\text { miss })]^{n-r}\)

Chapter 15, Section 15.4, Exercise 11 Page 1,202

Step 1

A person has a shooting of 9 out of 10 chance, and the probability of missing \(\frac{1}{10}\)

P(shoot)= \(\frac{9}{10}\)

P(miss)= \(\frac{1}{10}\)

To get the probability of shooting r times in n shoots, we came up with the formula:

⇒ \({ }_n C_r \cdot[P(\text { shoot })]^r \cdot[P(\text { miss })]^{n-r}\)

Chapter 15, Section 15.4, Exercise 1 Page 1,203

Step 1

Let

R be the event of getting a red face, and B be the event of getting a blue face. A fair cube has
4 red faces and 2 blue faces. We have the following probabilities:

P(R)= \(\frac{4}{6}=\frac{2}{3}\)

P(B)= \(\frac{2}{6}=\frac{1}{3}\)

When we roll the cube multiple times, we are doing multiple trials. To get the probabilities of multiple trials, we have:

⇒ \({ }_n C_r \cdot[P(A)]^r \cdot[P(B)]^{n-r}\)

Chapter 15, Section 15.4, Exercise 2 Page 1,204

Step 1

Let R be the event of getting a red face, and B be the event of getting a blue face. A fair cube has
4 red faces and 2 blue faces. We have the following probabilities:

P(R)= \(\frac{4}{6}=\frac{2}{3}\)

P(B)= \(\frac{2}{6}=\frac{1}{3}\)

When we roll the cube multiple times, we are doing multiple trials. To get the probabilities of multiple trials, we have:

⇒ \({ }_n C_r \cdot[P(A)]^r \cdot[P(B)]^{n-r}\)

Chapter 15, Section 15.4, Exercise 3 Page 1,205

Step 1

A tetrahedron has 3 blue faces and 1 red face. We have the following probabilities:

Chapter 15, Section 15.4, Exercise 4 Page 1,205

Step 1

Let R be the event of getting a red face, and B the event of getting a blue face.

A tetrahedron has 1 red face and 3 blue faces. We have the following probabilities:

P(R)= \(\frac{1}{4}\)

P(B)= \(\frac{3}{4}\)

When we roll the tetrahedron multiple times, we are doing multiple trials. To get the probabilities of multiple trials, we have:

⇒ \({ }_n C_r \cdot[P(A)]^r \cdot[P(B)]^{n-r}\)

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Chapter 15, Section 15.5, Exercise 1 Page 1,208

Step 1

The task is to calculate which of the given dartboards will give the player the highest probability of hitting the shaded area.

Chapter 15, Section 15.5, Exercise 2 Page 1,208

Step 1

The task is to determine the possible and the desired outcomes when the player throws a dart at a dart board.

Chapter 15, Section 15.5, Exercise 3 Page 1,209

Step 1

The task is to determine whether the given reasoning is correct or incorrect.

Chapter 15, Section 15.5, Exercise 4 Page 1,209

Step 1

The task is to determine the probability of hitting the shaded region of each of three given dartboards.

Chapter 15, Section 15.5, Exercise 5 Page 1,211

Step 1

The task is to determine which of the given three dartboards will make the competition most difficult.

Chapter 15, Section 15.5, Exercise 6 Page 1,212

Step 1

We are to find the probability of hitting the shaded part of this board:

Chapter 15, Section 15.5, Exercise 1 Page 1,213

Step 1

In a spinning wheel, there are 8 equal sections. Three sections will give you a chance of winning $100. Two sections will give you a chance of winning $200 and one section each for $300,$400, and $500

Chapter 15, Section 15.5, Exercise 2 Page 1,213

Step 1

In a spinning wheel, there are 8 equal sections. Three sections will give you a chance of winning $100 Two sections will give you a chance of winning $200 and one section each for $300, $400, and $500

Chapter 15, Section 15.5, Exercise 3 Page 1,213

Step 1

The task is to determine how often is expected to win a certain amount when the wheel is spun.

Chapter 15, Section 15.5, Exercise 4 Page 1,214

Step 1

In a spinning wheel, there are 8 equal sections. Three sections will give you a chance of winning $100. Two sections will give you a chance of winning $200, and one section each for $300, $400, and $500.

Chapter 15, Section 15.5, Exercise 1 Page 1,215

Step 1

We are either to keep $300 or to spin a wheel.

In a spinning wheel, there are 8 equal sections. Two sections will give you a chance of winning $100. The other 6 sections will give you $200, $300, $400, $500,$600 and $700

Chapter 15, Section 15.5, Exercise 2 Page 1,215

Step 1

We are either to keep $300 or to spin a wheel.

Chapter 15, Section 15.5, Exercise 1 Page 1,216

Step 1

We have a dartboard that has dimensions on its parts. Let us try to get the probability of each part.

Chapter 15, Section 15.5, Exercise 2 Page 1,219

Step 1

The task is to calculate the expected value for a 1 dart throw for the given dart board.

The post Carnegie Learning Section 15.5: Advanced Geometry Concepts – To Spin or Not to Spin appeared first on Answer Key for Math.

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