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

To find this probability, first determine the number of employees in area B who are not professionals. The number of skilled employees in area B is 90, and the number of elementary employees in area B is 80.

Thus, the total is:

$ext{Total in B and not professional} = 90 + 80 = 170.$

The probability is given by:

$P( ext{B and not professional}) = \frac{170}{1825} \approx 0.0931.$

Therefore, the probability that an employee is in area B and is not a professional is approximately 0.093.

To complete the Venn diagram using the given percentages:

• Calculate working from home:
  • Professionals (65%): $0.65 \times 740 = 481$
  • Skilled (40%): $0.40 \times 275 = 110$
  • Elementary (5%): $0.05 \times 260 = 13$
  • Summing gives total working from home = 481 + 110 + 13 = 604.

Assign relevant counts to the diagram based on the calculations while ensuring overlaps are accurately represented.

To find this probability, we first identify that R' is the complement of R (not from area A). Professionals total 740 + 380 = 1120. Thus:

$P(R' ∩ F) = \frac{380}{1825} \approx 0.208.$

Therefore, the probability is approximately 0.208.

To find this probability:

• First calculate the union of events H and R.

Using previously calculated data, the probability of neither working from home nor being from area A can be calculated with:

$P([H ∪ R]') = 1 - P(H) - P(R) + P(H ∩ R).$

After computations, the result is approximately 0.144.

This conditional probability can be computed by using the values obtained so far:

$P(F | H) = \frac{P(F ∩ H)}{P(H)}.$

Substituting known probabilities into the formula gives the final result: approximately 0.817.