Question

In a company, 20% of the employees are researchers and 30% of employees have Data Science diploma. 60% of researchers have Data Science researe diploma.

a) Estimate the proportion of employees who are researchers and have Data Science diploma.
b) Compute the proportion of Data Science diploma holders who are researchers.
c) Find the proportion of employees who either have Data Science diploma or are resecrch

Answer 1

a) The proportion of employees who are researchers and have a Data Science diploma is 12%. b) The proportion of Data Science diploma holders who are researchers is 2. c) The proportion of employees who either have a Data Science diploma or are researchers is 38%.

Step-by-step explanation:

To estimate the proportion of employees who are researchers and have a Data Science diploma, we need to multiply the proportion of employees who are researchers by the proportion of researchers with a Data Science diploma.

1. Proportion of researchers: 20% = 0.20
2. Proportion of employees with Data Science diploma: 30% = 0.30
3. Proportion of researchers with Data Science diploma: 60% = 0.60

a) Proportion of employees who are researchers and have a Data Science diploma = Proportion of researchers × Proportion of researchers with Data Science diploma = 0.20 × 0.60 = 0.12 = 12%

To compute the proportion of Data Science diploma holders who are researchers, we need to divide the proportion of researchers with a Data Science diploma by the proportion of employees with a Data Science diploma.

1. Proportion of researchers with Data Science diploma: 60% = 0.60
2. Proportion of employees with Data Science diploma: 30% = 0.30

b) Proportion of Data Science diploma holders who are researchers = Proportion of researchers with Data Science diploma ÷ Proportion of employees with Data Science diploma = 0.60 ÷ 0.30 = 2 = 2

To find the proportion of employees who either have a Data Science diploma or are researchers, we need to add the proportion of employees with a Data Science diploma and the proportion of researchers and subtract the proportion of employees who are both researchers and have a Data Science diploma.

1. Proportion of employees with Data Science diploma: 30% = 0.30
2. Proportion of researchers: 20% = 0.20
3. Proportion of employees who are researchers and have a Data Science diploma: 12% = 0.12

c) Proportion of employees who either have a Data Science diploma or are researchers = Proportion of employees with Data Science diploma + Proportion of researchers − Proportion of employees who are researchers and have a Data Science diploma = 0.30 + 0.20 - 0.12 = 0.38 = 38%