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\n0.25\n(type an integer or decimal rounded to two decimal places as needed.)\n(c) find the probability that a worker is in department b or is earning more than $80,000\n0.61\n(type an integer or decimal rounded to two decimal places as needed.)\n(d) find the probability that a worker is in department a or is earning $80,000 or less.\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\n0.25\n(type an integer or decimal rounded to two decimal places as needed.)\n(c) find the probability that a worker is in department b or is earning more than $80,000\n0.61\n(type an integer or decimal rounded to two decimal places as needed.)\n(d) find the probability that a worker is in department a or is earning $80,000 or less.\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

Number of workers in Department A is 49, and 6 in Department A earn more than $80,000. So number of workers in Department A earning $80,000 or less is $49 - 6=43$. Total number of workers is 110.

Step2: Calculate number of workers in Department B earning more than $80,000

Number of workers in Department B is $110 - 49 = 61$. 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 $61 - 34 = 27$.

Step3: Calculate number of workers in Department B or earning more than $80,000

Let $n(B)$ be number of workers in Department B ($n(B)=61$), $n(> 80000)$ be number of workers earning more than $80,000. Number of workers in Department B and earning more than $80,000 is 27. Using the formula $n(B\cup> 80000)=n(B)+n(> 80000)-n(B\cap> 80000)$. Number of workers earning more than $80,000 is $6 + 27=33$. So $n(B\cup> 80000)=61 + 33-27 = 67$. Probability $P=\frac{67}{110}\approx0.61$.

Step4: Calculate number of workers in Department A or earning $80,000 or less

Let $n(A)$ be number of workers in Department A ($n(A) = 49$), $n(\leq80000)$ be number of workers earning $80,000 or less. Number of workers in Department A and earning $80,000 or less is 43. Number of workers earning $80,000 or less is $110 - 33 = 77$. Using the formula $n(A\cup\leq80000)=n(A)+n(\leq80000)-n(A\cap\leq80000)$. So $n(A\cup\leq80000)=49+77 - 43=83$. Probability $P=\frac{83}{110}\approx0.75$.

Answer:

0.75