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The numbers 5, 8, 9, 9 and 9 are written on five different cards, as shown. If two of the cards are to be selected randomly, without replacement, what is the probability that the sum of the numbers on the two cards will be a multiple of 3?
Give your answer as a fraction.
p is the probability that event E will occur, and s is the probability that event E will not occur.

Quantity A

p+s

Quantity B

ps
A, B, and C are events in a probability experiment such that 0 < P(A) < 1, B and C are independent, and P(A) = 2P(B) = 3P(C).

Quantity A

$$\frac{2}{3}$$ P(A)

Quantity B

P(B or C)
In box H, there are 5 red balls, 3 green balls and 2 yellow balls, while In box R, there are 3 red balls and 7 yellow balls. If someone selects one ball from each box, what is the probability that he or she selects at least one yellow ball?
If one letter is to be randomly selected from the 7 letters in the word JOHNSON and one letter is to be randomly selected from the 5 letters in the word JONES, what is the probability that the two selections will be the same letter?
Give your answer as a fraction.
Set A: {71,73,79,83,87}
Set B: {57,59,61,67}
If one number is selected at random from set A, and one number is selected at random from set B, what is the probability that both numbers are prime?
20 boys and 40 girls are in Group A, while at least 7 boys, together with some girls are in Group B. To choose one person from each of the group, the probability that both are boys is no greater than $$\frac{1}{15}$$. Which of the following statements must be true?
Indicate all such statements.
A and B are independent events, and the probability that both events occur is $$\frac{1}{2}$$. Which of the following could be the probability that event A occurs?
Indicate all such probabilities.
Events A and B are independent. The probability that events A and B both occur is 0.6

Quantity A

The probability that event A occurs

Quantity B

0.3
A box contains 10 balls numbered from 1 to 10 inclusive. If Ann removes a ball at random and replaces it, and then Jane removes a ball at random, what is the probability that both women removed the same ball?
In a probability experiment, G and H are independent events. The probability that G will occur is r, and the probability that H will occur is s, where both r and s are greater than 0.

Quantity A

The probability that either G will occur or H will occur, but not both

Quantity B

r+s-r*s
A telephone system has $$n$$ telephone lines. For each of the $$n$$ lines, the event that the line will fail during a certain reliability test has probability 0.3, and these $$n$$ events are independent. If the probability that at least one of the n lines will not fail during the reliability test is greater than 0.99, what is the minimum value of $$n$$?
There are only identical number of red and green balls in a box. A person first randomly selects a ball from the box without replacement, and continues to select another ball. Which of the following probability is 1/2?
Indicate all that are true.
The probability that a component fails during first use is 0.1. If the component doesn`t fail during first use, then the probability that the component won`t fail in the following six months is 0.8

Quantity A

The probability that the component won`t fail within six months

Quantity B

0.75
The prizes for a certain contest are in 5 sealed envelopes: 2 containing cash and the other 3 containing gift certificates. If 2 envelopes are to be randomly selected from the 5 envelopes, one at a time without replacement, what is the probability that at least one of the envelopes selected will contain a cash prize?
Give your answer as a fraction.
In a box, the probability that the red ball is selected is $$\frac{5}{8}$$. Mark randomly selects balls twice from the box without replacement. If he didn`t get a red ball in the first attempt, then the probability that he gets a red ball in the second attempt is $$\frac{2}{3}$$. What is the probability that Mark get at least one red ball?(Another version: What is the probability that the first or the second ball selected will be red?)
Give your answer as a fraction.
Two balls are to be randomly selected from a bag, one at a time and without replacement. The probability that the first ball selected will be red is $$\frac{5}{8}$$. If the first ball selected is not red, the probability that the second ball selected will be red is $$\frac{2}{3}$$. What is the probability that the first or the second ball selected will be red (that is, one red ball either in the first attempt, or in the second attempt, but not both)?

Give your answer as a $$\underline{fraction}$$.
During each run of a computer simulation, either the letter X or the letter Y is displayed. For each run of the simulation, if the letter X is displayed, then the probability that X will be displayed in the next run is 0.3. Also for each run of the simulation, if the letter Y is displayed, then the probability that Y will be displayed in the next run is 0.4.

In 7 consecutive runs of the simulation, if X is displayed in the 5th run, what is the probability that X will be displayed in the 7th run?
For a certain probability experiment, the probability that event A will occur is $$\frac{1}{2}$$ and the probability that event B will occur is $$\frac{1}{3}$$. Which of the following values could be the probability that the event A∪B (that is, the event A or B, or both) will occur?
Indicate all such values.
The probability that Event A occurs is 0.63, while the probability that Event B occurs is 0.58. What is the greatest probability that Event A and B both occurs?
Give your answer as a decimal.

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