Agenetic test is used to determine if people have a predisposition for thrombosis, which is the formation of a blood clot inside a blood vessel that obstructs the flow of blood through the circulatory system. it is believed that 3% of people actually have this predisposition. the genetic test is 99% accurate if a person actually has the predisposition, meaning that the probability of a positive test result when a person actually has the predisposition is 0.99. the test is 98% accurate if a person does not have the predisposition. what is the probability that a randomly selected person who tests positive for the predisposition by the test actually has the predisposition?

The probability that a randomly selected person that tests positive for the predisposition by the test actually has the predisposition is : 0.6

i.e. P( Disease | positive ) = 0.6

Let : B = positive , A = disease

∴ P( A | B ) = P( B | A ) P ( A ) / P( B )

where : P( B | A ) = 0.99

             P ( A ) = 0.03

∴ P(Disease | positive ) = P ( positive |  disease ) * P( disease ) / P ( positive )

                                        =   (0.99) * (0.03) / P(positive )   ( 1 )  

Also  P( Positive ) = P( B | A ) P( A )+ P( B | no disease

)* P( no disease )  

                             = (0.99)*(0.03) + (0.02)* (0.97) = 0.049 ( 2 )

back to equation ( 1 )

P( Disease | positive ) = (0.99)* (0.03) / (0.049) = 0.6.

Hence the probability that a randomly selected person person who tests positive has the predisposition is 0.6

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answer: ice crystals in air

the water from the water body or another source of water gets evaporated as water vapor as an effect of heat on water. these water vapor rises in the upper layers of the earth atmosphere under high atmospheric pressure. the atmospheric pressure of these water molecules starts to decrease due to the effect of cold air. the invisible water vapor condenses into visible water droplets and ice crystals.these ice crystals and water droplets being less denser than the surrounding air floats on air as clouds.