Question

Allergic reactions to poison ivy can be miserable. plant oils cause the reaction. researchers at allergy institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. a random sample of 1000 people with known allergies to poison ivy participated in the study. oil from the poison ivy plant was rubbed on a patch of skin. for 500 of the subjects, it was washed off within 5 minutes. for the other 500 subjects, the oil was washed off after 5 minutes. the results are summarized in the table. reaction within 5 minutes after 5 minutes row total none 420 50 470 mild 60 330 390 strong 20 120 140 column total 500 500 1,000 what is the probability that a person selected at random had no reaction. express your answer as a decimal rounded to the nearest hundredth.

Answer 1

           reaction within 5 minutes        after 5 minutes       row total
none                 420                                  50                        470
mild                     60                                330                       390
strong                  20                                120                       140
column total      500                                 500                   1,000

What is the probability that a person selected at random had no reaction. 

470 / 1000 = 0.47
0.47 x 100% = 47%

There is a 47% probability that a person selected at random had no reaction. 

Answer 2

The probability that a person selected at random had no reaction $47\%$.

Further explanation:

The probability is the chance of any event.

The probability can be obtained as the ratio of favorable number of outcomes to the total number of outcomes

$\boxed{{\text{Probability}}=\frac{{{\text{Favorable number of outcome}}}}{{{\text{Total number of outcomes}}}}}$

Explanation:

A random sample of 1000 people with known allergies to poison ivy participated in the study.

The number of people that has reaction within 5 minutes is 500.

The number of people that has reaction after 5 minutes is 500.

420 people don’t show any reaction within 5 minutes.

60 people show mild reaction within 5 minutes.

20 people show strong reaction within 5 minutes.

50 people don’t show any reaction after 5 minutes.

330 people show mild reaction after 5 minutes.

120 people show strong reaction after 5 minutes.

The probability that a person selected at random had no reaction can be calculated as follows,

$\begin{aligned}{\text{Probability}}&=\frac{{470}}{{1000}}\\&= 0.47\\&= 47\%\\\end{aligned}$

Hence, the probability that a person selected at random had no reaction $47\%$.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: allergic reaction, poison ivy, allergy institute, washed, washing, effects, oil, random sample, rubbed, plant, probability, subjects, summarized, patch of skin.