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?

Solutions

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 1 year ago

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