Question

The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group $X$ consisted of $100$ people who observed early bedtimes, and Group $Y$ consisted of $100$ people who observed later bedtimes. If a person is chosen at random from those who recalled at least $1$ dream, what is the probability that the person belonged to Group $Y$?

• A. $\frac{68}{100}$
• B. $\frac{79}{100}$
• C. $\frac{79}{164}$
• D. $\frac{164}{200}$

Answer 1

The correct option is C $\frac{79}{164}$

Out of $200$ persons in the sample, those having atleast one dream are $200$$-$ those who had no dream, i.e. $200-36=164$

Now, out of $164$ people, those who belonged to group Y are $100-21=79$ people.

$\Rightarrow$ probability that the person chosen belonged to Group Y becomes $\frac{79}{164}$.