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Zorluk: KolayTwo-Way Tables and Probability

A survey of 80 commuters asked about their primary method of transportation to work and their commute distance. The results are summarized in the table below.

Commute DistanceBicycleWalkTotal
Under 1 mile152540
1 mile or more35540
Total503080

Based on the table, what fraction of the commuters who commute a distance of under 1 mile choose walking as their primary transportation method?

Cevap: 0.625

Cevap

5/8 or 0.625
To find the fraction of commuters who commute a distance of under 1 mile that choose walking, limit the sample space to the row representing 'Under 1 mile', which has a subtotal of 40 commuters. Within this row, 25 commuters walk. Thus, the fraction is 25/40, which simplifies to 5/8 (or 0.625).

Adım Adım Çözüm

1
Identify the conditional group (denominator).
The row 'Under 1 mile' has a total of 40 commuters.
The phrase 'of the commuters who commute a distance of under 1 mile' restricts the group of interest to only those in this row.
2
Identify the target group within the restricted group (numerator).
25 commuters choose walking.
Within the 'Under 1 mile' row, we look at the 'Walk' column.
3
Calculate the conditional fraction.
25/40 = 5/8 (or 0.625).
Divide the target count by the conditional group total to find the fraction.

Anahtar Kavram

Conditional Probability from a Two-Way Table
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