Question

2. (25 points) Statistical Independence, Conditional Probability, and Total Probability (a) A detection device consists of three sensors each with probability $p = 0.95$ of detecting a certain chemical such as carbon monoxide when it is present, independent of the other two sensors. The device sounds an alarm if a majority of the sensors detects the chemical. What is the probability that the device successfully detects the chemical if it is present?

          2. (25 points) Statistical Independence, Conditional Probability, and Total Probability
(a) A detection device consists of three sensors each with probability $p = 0.95$ of detecting a
certain chemical such as carbon monoxide when it is present, independent of the other two sensors.
The device sounds an alarm if a majority of the sensors detects the chemical. What is the
probability that the device successfully detects the chemical if it is present?

2. (25 points) Statistical Independence, Conditional Probability, and Total Probability
(a) A detection device consists of three sensors each with probability p = 0.95 of detecting a
certain chemical such as carbon monoxide when it is present, independent of the other two sensors.
The device sounds an alarm if a majority of the sensors detects the chemical. What is the
probability that the device successfully detects the chemical if it is present?

Added by James H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Robin Corrigan

06/11/2022

Step 1

95 of detecting the chemical when it is present. Therefore, the probability of a sensor not detecting the chemical is 1 - 0.95 = 0.05. Step 3: Determine the probability of the device successfully detecting the chemical To determine the probability of the device Show more…

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2. (25 points) Statistical Independence, Conditional Probability, and Total Probability (a) A detection device consists of three sensors, each with a probability p = 0.95 of detecting a certain chemical, such as carbon monoxide, when it is present, independent of the other two sensors. The device sounds an alarm if a majority of the sensors detect the chemical. What is the probability that the device successfully detects the chemical if it is present?