Question

part b
one student will be selected at random from the class.
consider the events:
x : the selected student is female
y : the selected student is right - handed
which statement about events x and y is true?
a. the events are independent because the number of right - handed students in the class is larger than the number of female students.
b. the events are independent because the number of categories for dominant hand is different from the number of categories for gender.
c. the events are not independent because the number of female students is 0.
d. the events are not independent because the probability of x is not equal to the probability of x given y.

Explanation:

• Option A: Events are independent if \(P(X\cap Y)=P(X)\times P(Y)\), not based on the number of categories. So this option is wrong.
• Option B: Independence is not determined by the difference in the number of categories. So this option is wrong.
• Option C: The number of female students being \(0\) is an extreme and not - related to the concept of independence. So this option is wrong.
• Option D: If \(P(X|Y)

eq P(X)\), then the events \(X\) (student is female) and \(Y\) (student is right - handed) are not independent.

Answer:

D. The events are not independent because the probability of \(X\) is not equal to the probability of \(X\) given \(Y\).