Using Statement (1), we can write the following equation:

Let x be the number of left handed people in the sample. 100-x is then the number of right handed people in the sample.

Therefore, the probability that a randomly selected person in the sample is left handed is:

Therefore Statement (1) is sufficient to answer the question

Statement (2) indicates that all women in the sample are right handed. This statement is not useful as it does not give the total number of right handed people in the sample.

Therefore, Statement (2) is not sufficient by itself to answer the question.

Only Statement (1) ALONE is sufficient.

(1) One third of the managers in the company are women.

Therefore the probability that the manager selected at random is a woman is .

Statement (1) alone is sufficient.

(2) Half of the employees in the company are women.

Even though half of the company's employees are women, this statement doesn't give the proportion of women who hold a manager job. Therefore, Statement (2) is not sufficient.

(1) 150 Employees have a MBA degree.

Since we do not know the number of employees at the company, we cannot determine the probability of employees who have an MBA degree. Statement (1) is not sufficient.

(2) 70 percent of employees do not have a MBA degree.

We can then determine the percentage of employees with an MBA degree as 30 percent. Therefore the probability of employees who have an MBA degree is 0.3.

Statement (2) ALONE is sufficient.

(1) Of all 1200 policyholders, 1050 did not have an accident.

From statement (1), we can determine that 150 policyholders had an accident. We can then calculate the probability as .

Statement (1) alone is sufficient.

(2) Of the policyholders who had an accident, 90% received a claim payment.

Statement (2) is irrelevant since we are not interested in the probability of policyholders who received a claim payment.

Statement (2) is not sufficient.

(1) 15 out of 150 light bulbs are defective.

Using statement (1), the probability of defective light bulbs is 

Statement (1) is sufficient.

(2) After checking half of the inventory, the store owner finds 10 defective light bulbs

We do not know the number of defective light bulbs in all the inventory and we do not know the number of light bulbs in inventory.

Statement (2) is not sufficient. 

(1) The number of adults in City A is 1000.

Statement (1) is not sufficient to find the number of unemployed adults in City A.

(2) Three fourth of adults in City A are employed.

This statement tell us that of adults are unemployed. However, without knowing the number of adults in City A we cannot determine the number of unemployed adults in City A. Statement (2) alone is not sufficient.

Combining both statements, we find that the number of unemployed adults is of 1000 which is 250.

Both statements together are sufficient, but neither statement alone is sufficient.

(1) Half of the men in the sample do not have a beard.

This statement implies that the other half of the men in the sample have a beard. Therefore, the probability that a randomly selected man in the sample has a beard is 0.5.

Statement (1) alone is sufficient. 

(2) There are 100 men with a beard in the sample.

Statement (2) gives us the number of men who have a beard in the sample but without knowing the number of men in the sample, we cannot find the probability of men who have a beard.

Statement (2) is not sufficient.

(1) 1000 of the students at the university are graduate students.

Statement (1) alone is not sufficient because we don't know the total number of students enrolled at the university.

(2) Only 20% of the students enrolled are graduate students.

Statement (2) gives the probability of graduate students enrolled at that university as 20%(0.2).

Statement (2) Alone is sufficient.

In order to calculate the probability the question asks for, we need to know the number of each color of marble.

I) Gives us the number of greens.

II) Gives us clues which will allow us to find the number of reds and yellows.

We need both statements to answer this question.

To find the desired probability we need to know which color cards were removed.

I) Tells us the number of black cards removed.

II) Tells us the number of red cards removed.

At first glance, we need both statements, but if we think for a minute, if we know the total number of cards removed and the number of one color removed, we can find the number of the color... So either statement works.