Statistics and Probability Answers

3. Ten married couples are in a room.

a) If two people are chosen at random find the probability that

(i) one is male and one is female, (ii) they are married to each other.

b) If 4 people are chosen at random, find the probability that 2 married couples are chosen.

c) If the 20 people are randomly divided into ten pairs, find the probability that each pair is a married couple.

In a survey conducted among a random sample of students the following observations were made regarding their gender and learning environment preferences during the COVID-19 pandemic: 168 prefer online learning 202 prefer face to face learning 180 prefer blended learning 34 male students prefer online learning and 70 male students prefer blended learning 106 female students prefer face to face learning Required: a) What is the probability that a female student is chosen? b) What is the probability that a male student prefers face to face learning? c) What is the probability that a student prefers online or blended learning? d) If it’s known that the student is female, what is the probability that this student prefers online learning. e) Using a practical example, explain the difference between mutually exclusive events and independent events.

The joint probability density function of X1 and X2 is

f(x1, X2) = c (2x1 + x2) 2 < x1 < 6, 0 < x2 < 5

0, otherwise

1 Find

(i) the value of c

(ii) Find P [3 < X1 < 4, X2 > 2]