The vice-president of a business firm has reviewed the records of the finn's personnel
and found that 70% of the employees read The Wall Street Journal. If the vice-president
was to choose 12 employees at random,what is the probability that the number of these
employees who read The Wall Street Journal is the following?
To calculate the probability of the number of employees who read The Wall Street Journal, we need to use the binomial probability formula. The formula is:
P(X = k) = (n C k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability that exactly k employees read The Wall Street Journal.
- n is the total number of employees chosen.
- p is the probability of an individual employee reading The Wall Street Journal.
- (n C k) is the number of ways to choose k employees from a total of n employees.
Let's calculate the probability for different values of k:
1. Probability that exactly 0 employees read The Wall Street Journal:
P(X = 0) = (12 C 0) * (0.7^0) * (1 - 0.7)^(12 - 0)
2. Probability that exactly 1 employee reads The Wall Street Journal:
P(X = 1) = (12 C 1) * (0.7^1) * (1 - 0.7)^(12 - 1)
3. Probability that exactly 2 employees read The Wall Street Journal:
P(X = 2) = (12 C 2) * (0.7^2) * (1 - 0.7)^(12 - 2)
And so on, until k reaches 12.
To calculate the binomial coefficients (n C k), you can use the formula:
(n C k) = n! / (k! * (n - k)!)
Using these formulas, you can calculate the probability for each k value.