Question

All of the workers at a warehouse work either part-time or full time. In addition, all of the workers work either the day shift or the evening shift. 60% of the workers work full time, and 25% work both full time and the day shift. An employee is chosen at random from all of the full-time workers. Given that the employee works full time, what is the probability that the employee works the day shift?

a) 0.40
b) 0.30
c) 0.15
d) 0.50

Answer 1

The probability that a randomly chosen full-time employee works the day shift is about 0.42, calculated using the conditional probability formula based on the given percentages of full-time workers and those working both full time and the day shift.

Step-by-step explanation:

The question asks us to find the probability that an employee works the day shift given that they work full time. We are told that 60% of the workers work full time and that 25% work both full time and the day shift. To find the desired probability, we use the definition of conditional probability. The formula is P(A|B) = P(A and B) / P(B), where P(A|B) is the probability of A given B, P(A and B) is the probability of both A and B happening, and P(B) is the probability of B.

In this case, full time employment is our B, and working full time and the day shift is A and B. Therefore, given that an employee works full time (the condition), the probability they also work the day shift is P(A and B) / P(B) = 25% / 60% = 0.4167 approximately, which simplifies to roughly 0.42 when rounding to two decimal places.

Answer:

The probability that an employee chosen at random from all of the full-time workers works the day shift is about 0.42, which is closest to option (a) 0.40.