SOLUTION: A survey conducted about job satisfaction showed that 20% of workers are not happy with their current jobs. Two workers are selected at random, and it is observed whether or not th

Algebra ->  Probability-and-statistics -> SOLUTION: A survey conducted about job satisfaction showed that 20% of workers are not happy with their current jobs. Two workers are selected at random, and it is observed whether or not th      Log On


   

Question 1152127: A survey conducted about job satisfaction showed that 20% of workers are not happy with their current jobs. Two workers are selected at random, and it is observed whether or not they are happy with their current jobs. What is the probability that of these two workers, at least one of them is happy with their current job?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The opposite of "at least one of the two is happy" is "both are unhappy".

The probability that both are unhappy is (0.2)(0.2) = 0.04; so the probability that at least one is happy is 1-0.04 = 0.96.

An alternative method for calculating the probability....

P(both happy) = (0.8)(0.8) = 0.64
P(A happy, B not happy) = (0.8)(0.2) = 0.16
P(A not happy, B happy) = (0.2)(0.8) = 0.16

P(at least one happy) = 0.64+0.16+0.16 = 0.96