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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.
The probability that Event A occurs is 0.45. What is the greatest possibility that Event A and Event B both occurs?
Give your answer as a decimal.
The probability that Event A occurs is 0.7, The probability that Event B occurs is 0.4. Which of the following could be the probability that Event A and B both occurs?
Indicate all such probabilities.
The probability that Event A occurs is 0.5, while the probability that Event B occurs is 0.3. What is the maximum possibility that both events do not occur?
If 125w + 25x + 5y + z = 264, and w, x, y and z are integers no less than 0 and no greater than 5, then the sum of w, x, y and z could be? Indicate all such values
If password TUKK is re-arranged, what is the probability that the password is re-arranged into the exact same as before?
Give your answer as a fraction.

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