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x > 0

P(R)=P(S)=x

P(T)=kx

Event R and T are mutually exclusive

Event R and S are independent

P(R or T) < P(R or S)

Quantity A

k

Quantity B

1-x


Two containers, each with some white and black balls. Container T includes 20 white and 30 black balls. When selecting one ball out of each box, the possibility of getting 2 white balls is 0.3, what is the probability of getting black ball from U?

Give your answer as a decimal.
A bag contains 6 balls of which 2 are red and 4 are green. If 2 balls are to be chosen at random one after the other, without replacement. what is the probability that the second ball chosen will be red?
A bag contains 13 blue pens and 3 red pens. Two pens are to be randomly selected from the bag, one at a time and without replacement. What is the probability that both of the pens selected will be blue?

Give your answer as a decimal.


A box contains 12 candies of four different flavors. The table above shows the numbers of candies of each flavor. If 2 candies are to be selected at random from the box, without replacement, what is the probability that of the 2 candies selected one will be a caramel candy and the other will be a cherry candy?
A jar contains at least 1 red marble and some black marbles. The number of black marbles is five times higher than that of red marbles. Five marbles are drawn in sequence, not replacing after each draw.

Quantity A

The number of red balls that are selected

Quantity B

The number of black balls that are selected


There are 5 gifts in a bag, of which 3 are cash and 2 are movie tickets, one person selects 2 of them without replacement. What is the probability that at least one cash bag could be selected?

Give your answer as a fraction.
A certain spacecraft has 2 separate computer systems, X and Y, each of which functions independently of the other. The probabilities that systems X and Y will function correctly at liftoff are 0.90 and 0.99, respectively. What is the probability that at least one system will function correctly at liftoff?
Event A and event B are independent. The probability that event A occurs is 0.6 and B occurs is 0.5. What is the probability that neither A nor B occurs?

Give your answer as a decimal.
The possibility of Event A occurs is 0.75, while the possibility of Event B occurs is 0.56. What is the maximum possibility that both events will occur?
a and b are distinct odd prime numbers.

Quantity A

The number of positive factors of $$2ab^{2}$$

Quantity B

The number of positive factors of $$a^{2}$$ $$b^{3}$$


How many of the multiples of 3 between 100 and 200 are odd integers?
Let n be a nonnegative integer such that when 6n is divided by 75, the remainder is 30. Which of the following is a list of all possible remainders when 7n is divided by 75?
The units digit of $$7^{n}$$ is r, and the units digit of $$9^{n}$$ is t, where n, r, and t are positive integers. Which of the following could be the value of r+t?

Indicate all such values.
Let q be a prime number less than 100. When q is divided by 5, the remainder is 2. When q is divided by 7, the remainder is 6, what is the remainder when q is divided by 8?
For all positive even integers n. n* represents the product of all even integers from 2 to n, inclusive. For example, 12*=12*10*8*6*4*2. What is the greatest prime factor of 20*+22*?
How many integers from 1 to 1000, inclusive, have the same remainder when divided by 2, 3, 5, 7?
How many integers between 100 and 1,000 are multiples of 7?
The sum of three different positive integers is 11.

Which two of the following statements together provide sufficient information to determine the three integers?

Indicate two such statements.
Z=$$123^{4}$$-$$123^{3}$$+$$123^{2}$$-123

What is the remainder when Z is divided by 122?
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