STATPRO HUMSS11-D W5 Review

Nine senior high students, seven college students, and five graduate students were invited to a seminar about mental health.

During the orientation, the students are to be seated in three rows of equal number. How many seating arrangements are possible when only senior high students can sit in the first row?

Answer explanation

There are 21 students altogether to be seated in 3 rows. There are the same number of students in each row which means there should be 7 students. This involves an ordinary permutation, where 7 Senior high students are chosen from 9 and are arranged.

Nine senior high students, seven college students, and five graduate students were invited to a seminar about mental health.

Two students will be asked for an interview. How likely is it that one interviewee is a college student while the other interviewee is a senior high or graduate student?

Answer explanation

There are 2 events that are involved here. 1st, choosing 1 college student, and the 2nd is choosing 1 non-college student. Both are computed using combinations, where we have the number of outcomes of the 1st event as 7C1 and the 2nd event has 14C1 outcomes. Since there are 21C2 ways of forming interviewees, the indicated answer is the probability we're looking for.

If P is the probability of an event, what is the probability of the event's complement?

Answer explanation

If P is the probability of an event, then its complement is 1-P.

Which of the following is/are true about a random variable X?

Answer explanation

The probabilities associated with the values of a random variable should be between 0 and 1, inclusive.

A box contains three red marbles and four green marbles. If two marbles are picked form the box, let R be the number of red marbles picked. What are the values of R?

• {1,2}

• {1,2,3,4,5,6,7}

• {0,1,2,3}

• {0,1,2}

Answer explanation

R={0,1,2}

Three coins are tossed. Let X be the number of times that the tails show up. Which of the following is the correct pmf?

• 
• 
• 
• 

Answer explanation

Refer to the possible outcomes of tossing three coins.

Answer explanation

2 is not a value of R, so the associated probaility is 0.

Answer explanation

Since all probabilities of a RV sum to 1, we can find the unknown probability by subtracting the known probabilities from 1.

Answer explanation

Use the sum of all probabilities (1) to solve for c.

Answer explanation