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Zorluk: KolayTwo-Way Tables and Probability

A medical study compared the effectiveness of two headache treatments, Treatment X and Treatment Y. The results of the study are shown in the table below.

TreatmentImprovedNo ImprovementTotal
Treatment X401050
Treatment Y351550
Total7525100

If a participant who received Treatment X is selected at random, what is the probability that the participant's headache improved?

  1. A
    15\frac{1}{5}
  2. B
    25\frac{2}{5}
  3. C
    815\frac{8}{15}
  4. 45\frac{4}{5}Cevap

Cevap

The correct answer is 45\frac{4}{5}.
The correct answer is the fraction expressing the number of participants who received Treatment X and improved (40) out of the total number of participants who received Treatment X (50), which simplifies to 45\frac{4}{5}.

Adım Adım Çözüm

1
Identify the total number of participants in the conditional group.
The total number of participants who received Treatment X is 5050.
The question specifies that a participant is selected from those who received Treatment X, which restricts the sample space to this row.
2
Identify the number of participants in that conditional group who experienced improvement.
There are 4040 participants who received Treatment X and experienced improvement.
We need to find the number of favorable outcomes within the restricted sample space.
3
Calculate the conditional probability.
The probability is 4050=45\frac{40}{50} = \frac{4}{5}.
Probability is the ratio of the number of favorable outcomes to the total number of possible outcomes in the restricted group.

Anahtar Kavram

Calculating conditional probability from a two-way table by identifying the restricted sample space.
Tahmini Süre:45s
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Konular

Two-Way Tables and Probability

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