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题目内容
40 DVDs (17 are about psychology, 14 are about biology, and 9 are about history) need to be arranged in a bookshelf such that the 9 history-related DVDs are, on the whole, arranged in chronological order. In how many ways can these DVDs be arranged?
Passwords for a certain computer consist of 5 symbols typed on a computer keyboard. Each password consists of one @ symbol, two # symbols, and two $ symbols, typed in any order. For example, @#$$# and $#$#@ are two different passwords for the computer. What is the total number of different passwords for the computer?
Among 50 spare parts. 2 are broken. What is the probability that both are broken when you select two spare parts from the total?
Give your answer as a fraction.
What is the ratio of a two-digit integer whose tens digit can be divisible by 2 to all the two-digit integers?
Give your answer as a fraction.
The total number of product A and B in a box is 20. The unit price of A and B is 0.2 and 0.4, respectively, and the total price of them is 5.6. What is the probability that someone randomly selects a product from the box and selects product A?
Give your answer as a fraction.
If one number is chosen at random from the first 1,000 positive integers, what is the probability that the number chosen has at least one digit with the number 6?
Give your answer as a fraction.
5 balls are in a box, including 1 red ball and 4 green balls. Of a volunteer picks up 2 balls randomly from the box, what is the probability that both balls are green?
Give your answer as a fraction.
Among 30 jackets, 10 are red, 10 are black and 10 are yellow. When selecting 5 out of these 30 jackets, what is the probability that 3 red jackets, 1 black jackets and 1 yellow jackets are selected?
Give your answer as a fraction.
What is the probability that a number whose tens digit is no more than 3 and units digit is no more than 4 is selected when selecting a number from 100 to 159 (inclusive)?
Give your answer as a fraction.
Set R={-3, -2, -1, 0, 1, 2, 3}
Set T={-7, -6, -5, -4, -3, -2}
If an integer is to be randomly selected from set S and an integer is to be randomly selected from set R, what is the probability that the product of the two integers selected will be positive?
Give your answer as a fraction.
From a class of 8 students, of which 5 students are female, a president and a vice president are to be chosen at random. If a student cannot be both the president and the vice president, what is the probability that the president and the vice president will both be female?
Give your answer as a fraction.
What is the probability that A and B are both selected when you randomly select 40 people out of a pool of 100 people (A and B included)?
Give your answer as a fraction.
Each digit of a 3-digit integer is a positive integer that is divisible by 3. What is the probability that the tens digit of such integers is an odd number and the hundreds digit of the integer is an even number?
Give your answer as a fraction.
Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer?
Each of the nine digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 is marked on a separate slip of paper and the nine slips are placed in a box. Three slips of paper will be randomly selected with replacement, and in the order selected the digits will be used to form a 3-digit number.

Quantity A

The probability that the 3-digit number will be greater than 600

Quantity B

$$\frac{4}{9}$$
The probability that a person will succeed at a particular task is $$p$$.

Quantity A

$$p(1-p)$$

Quantity B

$$0.4$$
Probability XX of Event A means the ratio of the probability that Event A occurs to the probability that Event A does not occur. If Probability XX of getting heads when tossing a coin is $$\frac{3}{7}$$, then what is the probability of getting heads when tossing the coin?
Give your answer as a fraction.
A and B are mutually independent and the probability that Event A occurs is the same as that of the probability that Event B occurs (both equals to 0.3).

Quantity A

The probability that Event A occurs when Event B does not occur

Quantity B

0.3
Both box T and box U have some white balls and black balls. There are 20 white balls and 30 black balls in box T. If a person selects 1 ball randomly from each box, then the probability that both balls are white is 0.25. What is the probability of selecting a black ball from the box U?
Give your answer as a fraction.
If the probability for each cannon shoots the target is 0.6, how many cannons shoot together can you ensure the overall probability of shooting the target reach 0.99?
Indicate all such choices.

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