the following data were gathered for 110 workers in two departments. of these workers, 49 were in department…

the following data were gathered for 110 workers in two departments. of these workers, 49 were in department a, 6 workers in department a earned more than $80,000, and 34 workers in department b earned $80,000 or less. complete parts (a) through (d) below\n(a) find the probability that a worker is in department a earning $80,000 or less\n0.39\n(type an integer or decimal rounded to two decimal places as needed.)\n(b) find the probability that a worker is in department b earning more than $80,000\n(type an integer or decimal rounded to two decimal places as needed.)

the following data were gathered for 110 workers in two departments. of these workers, 49 were in department a, 6 workers in department a earned more than $80,000, and 34 workers in department b earned $80,000 or less. complete parts (a) through (d) below\n(a) find the probability that a worker is in department a earning $80,000 or less\n0.39\n(type an integer or decimal rounded to two decimal places as needed.)\n(b) find the probability that a worker is in department b earning more than $80,000\n(type an integer or decimal rounded to two decimal places as needed.)

Answer

Explanation:

Step1: Calculate number of workers in Department A earning $80,000 or less

Total workers in Department A is 49 and 6 workers in Department A earned more than $80,000. So number of workers in Department A earning $80,000 or less is $49 - 6=43$.

Step2: Calculate total number of workers

Total number of workers is 110.

Step3: Calculate probability for part (a)

Probability $P(A_{80 -})=\frac{43}{110}\approx 0.39$ (already given and verified).

Step4: Calculate number of workers in Department B

Number of workers in Department B is $110 - 49 = 61$.

Step5: Calculate number of workers in Department B earning more than $80,000

Number of workers in Department B earning $80,000 or less is 34. So number of workers in Department B earning more than $80,000 is $61 - 34 = 27$.

Step6: Calculate probability for part (b)

Probability $P(B_{>80})=\frac{27}{110}\approx 0.25$

Answer:

(a) 0.39 (b) 0.25