The total number of balls in the box will be 

.

Since 

,

it follows that the number of balls is

 .

The frequencies out of 55 of each outcome from 1 to 10, in order, are as follows:

Their respective probabilities are their frequencies divided by 55:

.

The probability that the ball will be marked "5" is 

;

therefore, the probability that the ball will be marked with any given integer less than or equal to 5 will be greater than . 

The probability that the ball will be marked "6" is

 ;

therefore, the probability that the ball will be marked with any given integer greater than or equal to 6 will be less than . 

Therefore, it suffices to know whether the number on the ball is less than or equal to 5. Statement 2 states that the number on the ball is less than or equal to 5, so it is sufficient to answer the question in the affirmative. Statement 1 is insufficient, since there are primes less than or equal to 5 - 2, 3, and 5 - and one prime greater than 5, which is 7.

The total number of balls in the box will be 

.

Since 

,

it follows that the number of balls is

 .

The frequencies out of 55 of each outcome from 1 to 10, in order, is as follows:

Their respective probabilities are their frequencies divided by 55:

.

The probability that the ball will be marked "5" is 

;

therefore, the probability that the ball will be marked with any given integer less than or equal to 5 will be greater than . 

The probability that the ball will be marked "6" is

 ;

therefore, the probability that the ball will be marked with any given integer greater than or equal to 6 will be less than . 

Therefore, it suffices to know whether the number on the ball is less than or equal to 5.

Statement 1 alone is insufficient, since there are two perfect square integers from 1 to 5 (1 and 4) and one perfect square integer from 6 to 10 (9). Statement 2 alone is insufficient, since it is not clear whether the number on the ball is 5 or a number greater than 5. However, from the two statements together, it can be inferred that , and that the probability of drawing a ball with this number is .

Probability is a part to whole comparison.  

With statement 1, we don't know nor can we determine the probability of drawing a green marble because we know nothing about the probability of drawing a blue marble. Therefore, statement 1 is not sufficient.

With statement 2, we don't know nor can we determine anything regarding the probability of drawing a red marble. Therefore, statement 2 is not sufficient.

However, taken together, we can determine that the probability of drawing a green marble is . Therefore, BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 

Probability is the number of desired outcomes divided by the number of possible outcomes. 

With statement 1, we are told the probability of never flipping a head is , which is the same as always flipping a tail.  Since the probability of flipping a tail on a single flip is , we can determine the probability of flipping n tails is , which solves as  .  With n=3, we can solve for the probability of getting at least one tail is 1-probability of never getting a tail or 1-HHH:

.  

Therefore, statement 1 alone is sufficient.

With statement 2, we are told the probability of flipping at least one head is  . Since there are only 2 possible outcomes with each flip (heads or tails), the probability of flipping at least one head is the same as the probability of flipping at least one tail. Therefore, statement 2 alone is sufficient.

Therefore, the correct answer is EACH statement ALONE is sufficient.

He has 3 pants, 2 shirts, 2 hat choices (hat or no hat).

Each statement on its own gives us one equation with 2 unknowns, which is unsolvable. Therefore each statement alone is not sufficient.

The two equations are equivalent: x + y = 13 and 2.(x+y) = 2 x 13 = 26

Therefore we cannot sole for x and y either with both equations.

By the multiplication principle, the number of meals Jack can make is the product of the number of appetizers, the number of entrees, and the number of beverages. Statement 1 tells only the first two; Statement 2 does not give any of these quantities. From the two statements together, we know that there are seven appetizers, ten entrees, and seven beverages, so there are  possible Lunch Deal Meals.

Statement 1 alone gives irrelevant information; the cost of the Veggie Platter has no bearing on the number of possible combinations.

From Statement 2 alone, it can be determined that there are ten choices; therefore, the number of ways Lucy can order a Veggie Platter can be determined to be .

The only thing needed in order to answer the question is the number of vegetables from which Georgia has to choose. Neither statement alone gives this information.

However, it is possible to deduce this information from both statements together. From Statement 1, half the choices are "hearth healthy"; therefore, half are not. From Statement 2, this amounts to seven choices, so the total number of vegetables on the menu is fourteen, and there are a total of  possible Veggie Platters.

Each statement alone says that George can choose from ten vegetables - Statement 2 is different only in that it names three of them. George can choose any one of  different Veggie Platters.