We surveyed 100 workers at ABC Inc. We found that 70% are Male and 10% hold an M

Question

We surveyed 100 workers at ABC Inc. We found that 70% are Male and 10% hold an MBA degree.

Problem 1: We surveyed 100 workers at ABC Inc. we found that 70% are Male and 10% hold an MBA degree. In addition, among those who have MBA degrees, 60% of them are Male. Construct a two-way contingency table (use the pairs of events: MALE and FEMALE, MBA and NO MBA), and answer the following questions. Keep your answers in Fractions (DO NOT Simplifv) for Problem 1a) to 1e) a) Find the probability of a chosen worker, who is a MALE and also holds an MBA degree. (1 point) b) Find the probability of a chosen worker, who is a FEMALE and also holds an MBA degree. (1 point) c) Find the probability of a chosen worker, who is a MALE and does not hold an MBA degree. (1 point) d) Find the probability of a chosen worker, who is either a MALE or holds an MBA degree. (1 point) Find the probability of a chosen worker, who is neither a MALE nor holds an MBA degree. (1 point) e)

Explanation / Answer

Here we are given that 70% are males, therefore there would be 70 males and 30 females.

10% hold MBA, therefore 10 of the 100 people have an MBA here.

Now we are also given that among those holding an MBA, 60% are males, therefore 6 of the 10 MBA people are males and 4 females have an MBA. Therefore the table can noe be constructed as:

a) Probability that a person is male and also holds an MBA degree = 6 / 100 = 0.06 ( from the above table )

Therefore 0.06 is the required probability here.

b) Similar to above part, probability that a person is female and also has an MBA = 4/100 = 0.04

Therefore 0.04 is the required probability here.

c) Probability that a person is male and also does not hold an MBA degree = 64 / 100 = 0.64 ( from the above table )

Therefore 0.64 is the required probability here.

d) Probability that a person is either male or holds an MBA degree

= Probability that a person is male + Probability that a person is non male but has an MBA

= 0.7 + 0.04

= 0.74

Therefore 0.74 is the required probability here.

e) Probability who is neither male nor holds an MBA degree

= Probability that a person is female and does not hold an MBA degree

= 26 / 100

= 0.26

Therefore 0.26 is the required probability here.

Males Females MBA 6 4 No MBA 64 26

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