Question

Non-smoker 8 25 18 51 Light Smoker Medium Smoker Heavy Smoker Managerial Skilled Trades General Labor 21 94 83 198 19 26 28 59 24 31 62 26

3) Refer to the contingency table above. If 4 employees are randomly selected, what is the probability that at least one of them has a managerial job?

4) Refer to the contingency table above. If one employee from each of the four smoking categories is randomly selected, what is the probability that at least one of them has a managerial job?

Answer 1

3) If 4 employees are randomly selected, the probability that at least one of them has a managerial job

= 1 - P( none of the 4 employees has a managerial job)

$= 1 - \frac{177*176*175*174}{198*197*196*195}$

$= 0.363716$

4) If one employee from each of the four smoking categories is randomly selected,

The probability that at least one of them has a managerial job

= 1 - P( none of the 4 employees has a managerial job)

$= 1 - [\frac{(25+18)}{51}*\frac{(19+6)}{26}*\frac{(26+28)}{59}*\frac{(24+31)}{62}]$

$= 1 - [\frac{43}{51}*\frac{25}{26}*\frac{54}{59}*\frac{55}{62}]$

$= 1 - 0.658230$

$= 0.341770$