The two-way table shows the classification of students in a mathematics class by gender and dominant hand. A student who is ambidextrous uses both hands equally well.
\begin{tabular}{|l|c|c|c|c|}
\hline & Right-handed & Left-handed & Ambidextrous & Total \
\hline Male & 11 & 4 & 1 & 16 \
\hline Female & 12 & 2 & 0 & 14 \
\hline Total & 23 & 6 & 1 & 30 \
\hline
\end{tabular}
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?
The events are independent because the number of right-handed students in the class is larger than the number of female students.

The events are independent because the number of categories for dominant hand is different from the number of categories for gender.

The events are not independent because for one of the dominant hand categories the number of female students is 0 .

The events are not independent because the probability of $ X $ is not equal to the probability of $ X $ given $ Y $.

Question

The two-way table shows the classification of students in a mathematics class by gender and dominant hand. A student who is ambidextrous uses both hands equally well.
\begin{tabular}{|l|c|c|c|c|}
\hline & Right-handed & Left-handed & Ambidextrous & Total \
\hline Male & 11 & 4 & 1 & 16 \
\hline Female & 12 & 2 & 0 & 14 \
\hline Total & 23 & 6 & 1 & 30 \
\hline
\end{tabular}
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?
The events are independent because the number of right-handed students in the class is larger than the number of female students.

The events are independent because the number of categories for dominant hand is different from the number of categories for gender.

The events are not independent because for one of the dominant hand categories the number of female students is 0 .

The events are not independent because the probability of $ X $ is not equal to the probability of $ X $ given $ Y $.

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