The new cold medication was tested by giving 100 people the drug and 100 people a placebo. A control group consisted of 100 people who were given no treatment.The number of people in each group who showed improvement is shown in the table below. Cold drugPlaceboControlTotalImprovement705520145No improvement304580155Total100100100300 What is the probability that a randomly selected person in the study either was given the placebo or was in the control group?What is the probability that a randomly selected person improved?What is the probability that a randomly selected person was given the drug and improved?What is the probability that a randomly selected person who improved was given the drug?What is the probability that a randomly selected person who was given the drug improved?

Given data: The numbers of persons who were given a placebo are p=100. The numbers of persons who were in the control group are c=100. The numbers of persons who were given drugs are e=100. The total numbers of improved persons are i=145. The numbers of persons who were given drugs and improved are d=70. The total numbers of persons are T=300. 1) The expression for the probability that a person either was given the placebo or in the control group is, P(a)=pT+cT Substitute the given values in the above expression. P(a)=100300+100300=200300=23 Thus, the probability that a person either was given the placebo or in the control group is 2/3.2) The expression for the probability that the randomly selected person improved is, Pi=iT Substitute the given values in the above expression. Pi=145300=0.4833 Thus, the probability that the randomly selected person improved is 0.4833.3) The expression for the probability the numbers of persons who were given drugs and improved is, Pd=dT Substitute the given values in the above expression. Pd=70300=0.233 Thus, the probability of the number of persons who were given drugs and improved is 0.233.4) The expression for the probability that a person who improved given the drugs is, Pb=d/Ti/T Substitute the given values in the above expression. Pb=70/300145/300=70145=0.48275 Thus, the probability that a person who improved given the drugs is 0.48275. 5) The expression for the probability that a randomly selected person given drugs and improved is, Px=d/Te/T Substitute the given values in the above expression. Px=70/300100/300=70100=0.7 Thus, the probability that a randomly selected person given drugs and improved is 0.7.

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A First Course in Probability (10th Edition)

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ISBN:9780134753119

Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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The new cold medication was tested by giving 100 people the drug and 100 people a placebo. A control group consisted of 100 people who were given no treatment.

The number of people in each group who showed improvement is shown in the table below.

	Cold drug	Placebo	Control	Total
Improvement	70	55	20	145
No improvement	30	45	80	155
Total	100	100	100	300

What is the probability that a randomly selected person in the study either was given the placebo or was in the control group?
What is the probability that a randomly selected person improved?
What is the probability that a randomly selected person was given the drug and improved?
What is the probability that a randomly selected person who improved was given the drug?
What is the probability that a randomly selected person who was given the drug improved?

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The new cold medication was tested by giving 100 people the drug and 100 people a placebo. A control group consisted of 100 people who were given no treatment. The number of people in each group who showed improvement is shown in the table below.