Prove that
Is it possible to:
a) load two coins so that the probability of “heads” and “tails” were different, and the probability of getting any of the combinations “tails, tails,” “heads, tails”, “heads, heads” be the same?
b) load two dice so that the probability of getting any amount from 2 to 12 would be the same?
On a calculator keypad, there are the numbers from 0 to 9 and signs of two actions (see the figure). First, the display shows the number 0. You can press any keys. The calculator performs the actions in the sequence of clicks. If the action sign is pressed several times, the calculator will only remember the last click.
a) The button with the multiplier sign breaks and does not work. The Scattered Scientist pressed several buttons in a random sequence. Which result of the resulting sequence of actions is more likely: an even number or an odd number?
b) Solve the previous problem if the multiplication symbol button is repaired.
In a numerical set of
a) What is the smallest possible variance of such a set of numbers?
b) What should be the set of numbers for this?
The point
A high rectangle of width 2 is open from above, and the L-shaped domino falls inside it in a random way (see the figure).
a)
b)
The numbers
Prove that there is a number of the form
a)
b)
Of the four inequalities
Solve the inequality: