Select The Correct Answer.Ten Students Begin College At The Same Time. The Probability Of Graduating In Four Years Is 63 % 63\% 63% . Which Expanded Expression Shows The First And Last Terms Of The Expression Used To Find The Probability That At Least

Selecting the Correct Answer: Calculating the Probability of Graduating College

In this article, we will explore the concept of probability and how it is used to calculate the chances of certain events occurring. We will use a real-life scenario to demonstrate how to find the probability that at least one student will graduate from college in four years. The probability of graduating in four years is given as $63\%$, and we need to find the expression that represents the first and last terms of the probability that at least one student will graduate.

Let's break down the problem and understand what is being asked. We have ten students who begin college at the same time, and the probability of graduating in four years is $63\%$. This means that out of the ten students, $63\%$ of them will graduate in four years. We need to find the probability that at least one student will graduate from college in four years.

To calculate the probability that at least one student will graduate, we need to use the concept of complementary probability. The complementary probability is the probability that the event will not occur. In this case, the event is that at least one student will graduate. The complementary event is that no student will graduate.

The probability that no student will graduate is given by the expression $(1-p)^n$, where $p$ is the probability of graduating in four years and $n$ is the number of students. In this case, $p = 0.63$ and $n = 10$. Therefore, the probability that no student will graduate is:

$(1-0.63)^{10} = (0.37)^{10} = 0.0377$

Now that we have found the probability that no student will graduate, we can find the probability that at least one student will graduate by subtracting the complementary probability from $1$. This is given by the expression:

$1 - (1-p)^n = 1 - (0.37)^{10} = 1 - 0.0377 = 0.9623$

The expanded expression that shows the first and last terms of the expression used to find the probability that at least one student will graduate is:

$1 - (1-p)^n = 1 - (1-0.63)^{10} = 1 - (0.37)^{10}$

In this article, we have explored the concept of probability and how it is used to calculate the chances of certain events occurring. We have used a real-life scenario to demonstrate how to find the probability that at least one student will graduate from college in four years. The probability of graduating in four years is given as $63\%$, and we have found the expression that represents the first and last terms of the probability that at least one student will graduate.

• The probability of graduating in four years is $63\%$.
• The probability that no student will graduate is given by the expression $(1-p)^n$.
• The probability that at least one student will graduate is given by the expression $1 - (1-p)^n$.
• The expanded expression that shows the first and last terms of the expression used to find the probability that at least one student will graduate is $1 - (1-p)^n = 1 - (1-0.63)^{10} = 1 - (0.37)^{10}$.

• Q: What is the probability of graduating in four years? A: The probability of graduating in four years is $63\%$.
• Q: How do you calculate the probability that at least one student will graduate? A: You can use the concept of complementary probability to find the probability that at least one student will graduate.
• Q: What is the expanded expression that shows the first and last terms of the expression used to find the probability that at least one student will graduate? A: The expanded expression is $1 - (1-p)^n = 1 - (1-0.63)^{10} = 1 - (0.37)^{10}$.

• [1] Probability and Statistics, by James E. Gentle
• [2] Calculus, by Michael Spivak
• [3] Probability and Statistics, by William Feller
  Selecting the Correct Answer: Calculating the Probability of Graduating College

In this article, we will continue to explore the concept of probability and how it is used to calculate the chances of certain events occurring. We will use a real-life scenario to demonstrate how to find the probability that at least one student will graduate from college in four years. The probability of graduating in four years is given as $63\%$, and we need to find the expression that represents the first and last terms of the probability that at least one student will graduate.

Q: What is the probability of graduating in four years?

A: The probability of graduating in four years is $63\%$.

Q: How do you calculate the probability that at least one student will graduate?

A: You can use the concept of complementary probability to find the probability that at least one student will graduate. The complementary probability is the probability that the event will not occur. In this case, the event is that at least one student will graduate. The complementary event is that no student will graduate.

Q: What is the expression that represents the probability that no student will graduate?

A: The expression that represents the probability that no student will graduate is $(1-p)^n$, where $p$ is the probability of graduating in four years and $n$ is the number of students. In this case, $p = 0.63$ and $n = 10$. Therefore, the probability that no student will graduate is:

$(1-0.63)^{10} = (0.37)^{10} = 0.0377$

Q: How do you find the probability that at least one student will graduate?

A: To find the probability that at least one student will graduate, you can subtract the complementary probability from $1$. This is given by the expression:

$1 - (1-p)^n = 1 - (0.37)^{10} = 1 - 0.0377 = 0.9623$

Q: What is the expanded expression that shows the first and last terms of the expression used to find the probability that at least one student will graduate?

A: The expanded expression that shows the first and last terms of the expression used to find the probability that at least one student will graduate is:

$1 - (1-p)^n = 1 - (1-0.63)^{10} = 1 - (0.37)^{10}$

Q: What is the significance of the probability that at least one student will graduate?

A: The probability that at least one student will graduate is an important concept in probability theory. It represents the likelihood that at least one student will graduate from college in four years. This probability can be used to make informed decisions about college admissions, financial aid, and other related issues.

Q: How can you apply the concept of probability to real-life scenarios?

A: The concept of probability can be applied to a wide range of real-life scenarios, including finance, insurance, medicine, and engineering. For example, you can use probability to calculate the likelihood of a stock price increasing or decreasing, or to determine the probability of a patient responding to a certain treatment.

Q: What are some common applications of probability in real-life scenarios?

A: Some common applications of probability in real-life scenarios include:

• Calculating the probability of a stock price increasing or decreasing
• Determining the probability of a patient responding to a certain treatment
• Calculating the probability of a natural disaster occurring
• Determining the probability of a product failing or succeeding in the market

In this article, we have explored the concept of probability and how it is used to calculate the chances of certain events occurring. We have used a real-life scenario to demonstrate how to find the probability that at least one student will graduate from college in four years. The probability of graduating in four years is given as $63\%$, and we have found the expression that represents the first and last terms of the probability that at least one student will graduate.

• The probability of graduating in four years is $63\%$.
• The probability that no student will graduate is given by the expression $(1-p)^n$.
• The probability that at least one student will graduate is given by the expression $1 - (1-p)^n$.
• The expanded expression that shows the first and last terms of the expression used to find the probability that at least one student will graduate is $1 - (1-p)^n = 1 - (1-0.63)^{10} = 1 - (0.37)^{10}$.

• Q: What is the probability of graduating in four years? A: The probability of graduating in four years is $63\%$.
• Q: How do you calculate the probability that at least one student will graduate? A: You can use the concept of complementary probability to find the probability that at least one student will graduate.
• Q: What is the expanded expression that shows the first and last terms of the expression used to find the probability that at least one student will graduate? A: The expanded expression is $1 - (1-p)^n = 1 - (1-0.63)^{10} = 1 - (0.37)^{10}$.

• [1] Probability and Statistics, by James E. Gentle
• [2] Calculus, by Michael Spivak
• [3] Probability and Statistics, by William Feller