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whats the answer to this question i probability?

According to research, heart attack is one of the leading causes of death worldwide with about 7.6 million casualties in 2013. The research also claimed that “male smokers are likely to experience heart attack 15 times more than those who don’t smoke and female smokers are likely to experience heart attack 12 times more than nonsmoking females.” Furthermore, the National Statistics Office released data that 16% of females worldwide are smokers. Suppose you’re in a hospital, waiting for your turn for a medical checkup, and the female beside you is having a monthly maintenance checkup following a heart attack. What are the chances that she is a smoker?

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This is all conditional probability

probability of a NONsmoking woman having a heart attack = p say, and you don’t even need to put a value on p

probability of a smoking woman having a heart attack = p

probability of a woman having a heart attack

= (proportion of smokers) x (probability of a smoking woman having a heart attack)+(proportion of NON-smokers) x (probability of a NON-smoking woman having a heart attack)

=0.84 p +12 x 0.16 x p =2.76 p

your answer is 1.92p/2.76p = 0.695652174

i,e, 69.57%

16x 12 p =192 p

192/(84+192)=192/276 =.695652174

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It’s an application of Bayes’ Theorem.

Simplify the complicated side; don't complify the simplicated side.

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