A company has 1825 employees - Edexcel - A-Level Maths Statistics - Question 5 - 2022 - Paper 1

To find the probability that an employee lives in area B and is not a professional, we first find the number of employees in area B that are not professionals:

• Skilled in B: 90
• Elementary in B: 80

Thus, the total is: $90 + 80 = 170$

Now, we use the total number of employees: $P(B \cap Not\ Professional) = \frac{170}{1825} \approx 0.093 \text{ or } 9.3\%$

Using the provided probabilities for working from home:

• Professional working from home = 65% of 1120 = 481
• Skilled working from home = 40% of 365 = 146
• Elementary working from home = 5% of 340 = 17

The completed sections of the Venn diagram are:

• Section F: 481
• Section H: 146
• Section R: 130
• Intersection areas shaded accordingly.

To find this probability, we note that R' is the complement of area A, which includes:

• Professional in area B = 380

Thus: $P(R' ∩ F) = \frac{380}{1825} \approx 0.208 \text{ or } 20.8\%$

To find this probability, we note the total must exclude those in areas H and R. Given the data:

• Total without H or R = Employees not working from home and not in area A

Using the values: $P([H \cup R]') = \frac{133 + 130}{1825} \approx 0.144 \text{ or } 14.4\%$

To find the probability of being a professional given that the employee works from home: $P(F | H) = \frac{P(F \cap H)}{P(H)}$ Using the appropriate values from above, we would compute this accordingly and find:

• Total professionals working from home = 481,
• Total working from home = 481 + 146 + 17 = 644 Thus: $P(F | H)= \frac{481}{644} \approx 0.747 \text{ or } 74.7\%$