An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Identify the correct conditional probability: P(positive mammogram | no cancer) = 0.09.
Use the table to find the number of women with cancer and a positive mammogram (211,200) and the total number of women with a positive mammogram (4,689,600).
Calculate P(cancer | positive mammogram) = 4 , 689 , 600 211 , 200 .
Round the result to three decimal places: 0.045 .
Explanation
Identify the correct conditional probability (a) The probability of receiving a positive mammogram given cancer is not present is 0.09 . This is a false positive. This is expressed as P(positive mammogram | no cancer) = 0.09. So the correct choice is A.
Verify the table (b) The table is already filled with the correct values.
Calculate the conditional probability (c) We want to compute P(cancer | positive mammogram). Using the table, we have: Number of women with cancer and a positive mammogram = 211,200 Total number of women with a positive mammogram = 4,689,600 So, P(cancer | positive mammogram) = 4 , 689 , 600 211 , 200
Calculate the fraction Now, we calculate the value of the fraction: 4 , 689 , 600 211 , 200 ≈ 0.04503
Round the result Rounding to three decimal places, we get 0.045.
Examples
Imagine you're a doctor trying to interpret mammogram results. This calculation helps you determine the likelihood that a patient actually has cancer if their mammogram comes back positive. It's crucial for making informed decisions about further testing and treatment. For example, if a patient has a positive mammogram, the probability of them actually having cancer is calculated as follows: P ( " c an cer "∣" p os i t i v e mamm o g r am " ) = " T o t a l n u mb ero f w o m e n w i t ha p os i t i v e mamm o g r am " " N u mb ero f w o m e n w i t h c an cer an d a p os i t i v e mamm o g r am " = 4 , 689 , 600 211 , 200 ≈ 0.045 . This means there's about a 4.5% chance they have cancer, even with a positive result.
A device delivering a current of 15.0 A for 30 seconds allows approximately 2.81 x 10^21 electrons to flow through it. This is calculated by first finding the total charge using the formula Q = I × t, which gives Q = 450 C. Then, converting the charge to the number of electrons using the charge of a single electron results in the final count.
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