Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

testing for a disease can be made more efficient by combining samples. If the samples from two people are combined and the mixture tests​ negative, then both samples are negative. On the other​ hand, one positive sample will always test​ positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.15​, find the probability of a positive result for two samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely​ necessary?w./search?q=%E2%80%8B"At+least%E2%80%8B+one"+is+equivalent+to%E2%80%8B+_______.&oq=%E2%80%8B"At+least%E2%80%8B+one"+is+equivalent+to%E2%80%8B+_______.&aqs=chrome..69i57j0i22i30l3.409j0j4&sourceid=chrome&ie=UTF-8 The probability of a positive test result is nothing

Sagot :

Answer:

(a) [tex]P(Two\ Positive) = 0.2775[/tex]

(b) It is not too low

Step-by-step explanation:

Given

[tex]P(Single\ Positive) = 0.15[/tex]

[tex]n = 2[/tex]

Solving (a):

[tex]P(Two\ Positive)[/tex]

First, calculate the probability of single negative

[tex]P(Single\ Negative) =1 - P(Single\ Positive)[/tex] --- complement rule

[tex]P(Single\ Negative) =1 - 0.15[/tex]

[tex]P(Single\ Negative) =0.85[/tex]

The probability that two combined tests are negative is:

[tex]P(Two\ Negative) = P(Single\ Negative) *P(Single\ Negative)[/tex]

[tex]P(Two\ Negative) = 0.85 * 0.85[/tex]

[tex]P(Two\ Negative) = 0.7225[/tex]

Using the complement rule, we have:

[tex]P(Two\ Positive) = 1 - P(Two\ Negative)[/tex]

So, we have:

[tex]P(Two\ Positive) = 1 - 0.7225[/tex]

[tex]P(Two\ Positive) = 0.2775[/tex]

Solving (b): Is (a) low enough?

Generally, when a probability is less than or  equal to 0.05; such probabilities are extremely not likely to occur

By comparison:

[tex]0.2775 > 0.05[/tex]

Hence, it is not too low

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.