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题目内容
How many different 5-digit numbers can be formed by one "1",two "2",and two "3"?
The letters in a certain name can be arranged in exactly 180 different orders. Which of the following could be that name?


Several 0 and 1 are arranged in a 10*10 palace as follows. Among all the number 0, what is the probability that the selected 0 is located where the number of 0 in that row is odd while the number of 0 in that column is also odd?

Give your answer as a fraction.
In a box of red, blue and green balls, if the ratio of red to blue is 2:3, the ratio of blue to green is 4:3, then what ratio of all balls in the box are blue ones?

Give your answer as a fraction.
The vehicles of Company W are numbered consecutively from 1 to 650. The vehicles with a number that ends with one of the digits 1, 2, 3, 4, or 5 are used by Division 1. Vehicles with a number between 130 and 389, inclusive, are trucks. What percent of the company vehicles are trucks used by Division 1?
Three numbers are to be selected at random and without replacement from the five numbers 4, 5, 7, 8 and 11. What is the probability that the three numbers selected could be the lengths of the sides of a triangle?
What is the probability that the one 3-digit and one 2-digit integers that could be formed out of 1, 2, 3, 4 and 5 (each figure is used for only once) are both even integers?

Give your answer as a fraction.
When randomly selecting four different integers from 1 to 9, inclusive, the probability that 1, 2, 3 and 4 are selected in the above order is x, while the probability that 1,2 3 and 4 are selected no matter in what order is y. What is the ratio of x to y?

Give your answer as a fraction.
Event A and B are complementary events. The probability that event A occurs is p, while the probability that event B occurs is 2p

Quantity A

p

Quantity B

1-p
p is a value of probability greater than 0.5

Quantity A

2p

Quantity B

$$p^{2}$$
In a probability experiment, $$R$$, $$S$$, and $$T$$ are events such that $$P(S)=P(T)=x$$, $$P(R)=kx$$, and $$P(R$$ or $$S) \lt P(S$$ or $$T)$$, where $$k$$ and $$x$$ are positive numbers. Events $$R$$ and $$S$$ are mutually exclusive, and events $$S$$ and $$T$$ are independent.

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 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 only red marbles and black marbles. The jar contains more than one red marble and 5 times as many black marbles as red marbles. Five marbles are to be selected from the jar without replacement.

Quantity A

Of the marbles selected, the number that will be red

Quantity B

Of the marbles selected, the number that will be black
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 0.58. 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 $$a^{2}$$ $$b^{3}$$

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