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Gre4nikov [31]
3 years ago
5

ATCs are required to undergo periodic random drug testing.

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
8 0

Answer:

The responsess to the given question can be defined as follows:

Step-by-step explanation:

P(medication\ used) = 0.007 \\\\P( drug \not\ used ) = 1 - 0.007 = 0.993\\\\P(test\ positive  | medication \ used) = 0.96 \\\\ P(test \ negative | medication \ used) = 1 - 0.96 = 0.04\\\\

P(Point | Non-used\ medication )=0.93\\\\ P(Point |No\ medication ) = 1 - 0.93 = 0.07

As per the given info we draw the tree diagram which is defined in the attachment file.

P ( test \ is\  positive ) = P( medication \ used ) \times P( Test \ positive | medication \ used ) + P( medication not \ used ) \times  P( Test\ positive | medication \ not \ used )

                  = ( 0.007 \times 0.96 ) + ( 0.993\times 0.07 )\\\\= 0.0762

P( medication \ used | test\ positive )= \frac{\textup{P( medication used ) *P( Test positive given medication  used )}}{\textup{P( medication used )}}  

= \frac{( 0.007\times 0.96 )}{0.0762}\\\\= 0.0882

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