Math  /  Data & Statistics

QuestionDreams Recalled during One Week \begin{tabular}{|l|c|c|c|c|} \hline & None & 1 to 4 & 5 or more & Total \\ \hline Group X & 15 & 28 & 57 & 100 \\ \hline Group Y & 21 & 11 & 68 & 100 \\ \hline Total & 36 & 39 & 125 & 200 \\ \hline \end{tabular}
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\mathrm{Y}^{\prime} ? A) 68100\frac{68}{100} B) 79100\frac{79}{100} C) 79164\frac{79}{164} D) 164200\frac{164}{200}

Studdy Solution

STEP 1

1. We are only considering people who recalled at least 1 dream.
2. Group Y Y' refers to Group X, as it is the complement of Group Y.

STEP 2

1. Calculate the total number of people who recalled at least 1 dream.
2. Calculate the number of people in Group X who recalled at least 1 dream.
3. Calculate the probability that a person who recalled at least 1 dream is from Group X.

STEP 3

Calculate the total number of people who recalled at least 1 dream:
Total with 1 to 4 dreams+Total with 5 or more dreams=39+125=164\text{Total with 1 to 4 dreams} + \text{Total with 5 or more dreams} = 39 + 125 = 164

STEP 4

Calculate the number of people in Group X who recalled at least 1 dream:
Group X with 1 to 4 dreams+Group X with 5 or more dreams=28+57=85\text{Group X with 1 to 4 dreams} + \text{Group X with 5 or more dreams} = 28 + 57 = 85

STEP 5

Calculate the probability that a person who recalled at least 1 dream is from Group X:
Number in Group X who recalled at least 1 dreamTotal number who recalled at least 1 dream=85164\frac{\text{Number in Group X who recalled at least 1 dream}}{\text{Total number who recalled at least 1 dream}} = \frac{85}{164}
Since Group Y Y' refers to Group X, the probability is:
85164\boxed{\frac{85}{164}}
However, none of the provided options match this probability. Let's verify if the problem asks for a different calculation or if there is an error in the options.

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