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你能说中文吗

Apr 10, 2024

你能说中文吗

当然可以！我会说中文。你有什么数学问题想问吗？

你能不能帮我解决excel里的问题

当然可以！请问你在Excel里遇到了什么数学问题呢？我会尽力帮助你解决的。

Performance enhancing drugs in athletes is a big issue and has been around for some time. One estimate is that 5% of all athletes use drugs (D) which means 95% are clean (C). In professional sports athletes are tested regularly, and some athletes who are clean test positive (P), and some who use drugs test negative (N) – false positives and false negatives. In relation to the reliability of testing it is estimated that 3% of Clean athletes test positive and 8% of Drug Takiing athletes test negative. P(P/C) = 0.03 and P(N/D) = 0.08. Note this implies P(N/C) = 0.97 a. Calculate the probability that an athlete is a Drug user and they test Positive b. Calculate the probability that an athlete is Clean and they test Negative c. Calculate the probability that an athlete is Clean or they test Negative d. From the calculations so far, construct a joint probability table comparing athlete status and their testing status i.e. fill out the table below. Show all calculations

Solution by Steps

step 1

Given P(D) = 0.05 and P(P/D) = 1 - P(N/D) = 1 - 0.08 = 0.92. To find P(D and P), we multiply P(D) by P(P/D)

step 2

Calculate P(D and P) = P(D) * P(P/D) = 0.05 * 0.92

step 3

Simplifying the expression: P(D and P) = 0.05 * 0.92 = 0.046

Answer

P(D and P) = 0.046

Key Concept

Joint Probability of Independent Events

Explanation

The joint probability of two independent events, A and B, is the product of their individual probabilities: P(A and B) = P(A) * P(B).

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step 1

Given P(C) = 0.95 and P(N/C) = 0.97. To find P(C and N), we multiply P(C) by P(N/C)

step 2

Calculate P(C and N) = P(C) * P(N/C) = 0.95 * 0.97

step 3

Simplifying the expression: P(C and N) = 0.95 * 0.97 = 0.9215

Answer

P(C and N) = 0.9215

Key Concept

Joint Probability of Independent Events

Explanation

The joint probability of two independent events, A and B, is the product of their individual probabilities: P(A and B) = P(A) * P(B).

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step 1

Given P(C) = 0.95, P(N) = P(D and N) + P(C and N), where P(D and N) = P(D) * P(N/D) = 0.05 * 0.08

step 2

Calculate P(D and N) = 0.05 * 0.08 = 0.004

step 3

We already have P(C and N) from previous calculation, which is 0.9215

step 4

Calculate P(N) = P(D and N) + P(C and N) = 0.004 + 0.9215

step 5

Simplifying the expression: P(N) = 0.004 + 0.9215 = 0.9255

step 6

To find P(C or N), we use the formula P(C or N) = P(C) + P(N) - P(C and N)

step 7

Calculate P(C or N) = 0.95 + 0.9255 - 0.9215

step 8

Simplifying the expression: P(C or N) = 0.95 + 0.9255 - 0.9215 = 0.954

Answer

P(C or N) = 0.954

Key Concept

Probability of Union of Two Events

Explanation

The probability of the union of two events, A or B, is given by P(A or B) = P(A) + P(B) - P(A and B).

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step 1

To construct the joint probability table, we use the probabilities calculated in the previous steps

step 2

The table will have four entries: P(D and P), P(D and N), P(C and P), and P(C and N)

step 3

We have P(D and P) = 0.046 and P(C and N) = 0.9215 from previous calculations

step 4

We also have P(D and N) = 0.004. To find P(C and P), we use P(C and P) = P(C) * P(P/C) = 0.95 * 0.03

step 5

Calculate P(C and P) = 0.95 * 0.03 = 0.0285

step 6

Now we can fill out the table with the calculated probabilities

Answer

Joint Probability Table: | Status/Test | Positive (P) | Negative (N) | |-------------|--------------|--------------| | Drug (D) | 0.046 | 0.004 | | Clean (C) | 0.0285 | 0.9215 |

Key Concept

Joint Probability Table

Explanation

A joint probability table displays the probability of each combination of outcomes for two events.