Question

In: Statistics and Probability

A student club has 65 members; of these members, 28 are male and22 are freshmen....

A student club has 65 members; of these members, 28 are male and 22 are freshmen. Of the males, 10 are also freshmen.

What is the probability that a randomly selected student in the club is a freshman?
What is the probability that a randomly selected student in the club is a male or a freshman?
What is the probability that a randomly selected student in the club is male given that the student is a freshman?
What is the probability that a randomly selected student in the club is male and a freshman?

Expert Solution

Let us define the following events:
M: a randomly selected student in the club is male; and

F: a randomly selected student in the club is a freshman.

Now, out of a total of 65 members 28 are male => P(M) = 28/65

Moreover, out of a total of 65 members 22 are freshmen => P(F) = 22/65

Moreover, out of a total of 65 members 10 are both male and freshmen => P(M∩F) = 10/65

Part 1.

The probability that a randomly selected student in the club is a freshman is given by:

P(F) = 22/65 [ANSWER]

Part 2.

The probability that a randomly selected student in the club is a male or a freshman is given by:

Part 3.

The probability that a randomly selected student in the club is male given that the student is a freshman is given by:

Part 4.

The probability that a randomly selected student in the club is male and a freshman is given by:

orchestra answered 2 years ago

A student club has 65 members; of these members, 28 are male and 22 are freshmen....

A student club has 65 members; of these members, 28 are male and 22 are freshmen. Of the males, 10 are also freshmen. Answer the questions below as a fraction in the form numerator/denominator. Hint: it may be useful to create your own cross tabulation table. What is the probability that a randomly selected student in the club is a freshman? What is the probability that a randomly selected student in the club is a male or a freshman? What...

A club has 50 members of which 20 are freshmen, 15 are sophomores, 10 are juniors...

A club has 50 members of which 20 are freshmen, 15 are sophomores, 10 are juniors and 5 are seniors. a) How many ways are there to select a president, a senior vice president, and a vice president if they can not be from the same class? b) How many ways are there to select one president, and two vice presidents if they can not be from the same class?

Independent random samples were taken of male and female members of University Entrepreneurship Club. These members...

Independent random samples were taken of male and female members of University Entrepreneurship Club. These members were considering starting a business. Of 500 members, 150 actually started a business venture. Estimate the value of the population proportion. (Round your answers to 3 decimal places.) Develop a 99% confidence interval for the population proportion.

A chess club has 36 members. Members are categorized as Novice members, Regular members, and Master...

A chess club has 36 members. Members are categorized as Novice members, Regular members, and Master members. There are 8 Novice members, 21 Regular members, and 7 Master members in the club. For each part below, you must include a few words that describe your counting strategy. A number only as a response will not receive full credit. (a) How many committees of size 5 can be chosen if the committee must have 1 Novice, 2 Regular, and 2 Master...

1) A club is choosing 2 members to serve on a committee. The club has nominated...

1) A club is choosing 2 members to serve on a committee. The club has nominated 2 women and 2 men. Based on chance alone, what is the probability that one woman and one man will be chosen to be on the committee? rounded to 4 decimal places 2) A club is choosing 2 members to serve on a committee. The club has nominated 2 women and 2 men. Based on chance alone, what is the probability no women are...

The Club has 9 members. The club needs to elect a President, Vice President, Secretary and...

The Club has 9 members. The club needs to elect a President, Vice President, Secretary and Treasurer, how many different ways are possible? How many ways are there to find a committee of size three. The Club has 10 members, 3 freshman, 4 sophomores and 3 juniors. How many ways are there to find a committee of size three with no freshmen? How many ways are there to find a committee of size three with one freshmen?

In a club with 8 male and 10 female members, how many 4-member committees can be...

In a club with 8 male and 10 female members, how many 4-member committees can be chosen that have (a) at least 3 women? (b) no more than 2 men?

A club with 23 members is voting on a proposal. A group of 5 has decided...

A club with 23 members is voting on a proposal. A group of 5 has decided to vote in favor of the proposal while each of the rest of the members vote independently with a chance of 44% in favor of the proposal. What are the chances that the proposal will get the majority vote.

The book club of the month has determined that a quarter of its members purchase the...

The book club of the month has determined that a quarter of its members purchase the line offered as a monthly selection. if a random sample of 300 members is selected, what is the probability that: a) more than 0.18 of the members will buy the selected book b) less than 0.28 of the members will buy the selected book c) within which limits of the population proportion will be found 99% of the sample proportions d) if the club...

A country club has a membership of 500 members and operates facilities that include a swimming...

A country club has a membership of 500 members and operates facilities that include a swimming pool and a gymnasium. The club president would like to know how many members regularly use the facilities. A survey of the members indicates that 70% regularly use the swimming pool (S), 50% regularly use the gymnasium (G), and 5% use neither of these facilities regularly. Calculate the probability of the club members who use the facilities of the swimming pool and gymnasium P(S∩G). ...