There are two symmetrical cubes. Is it possible to write some numbers on their faces so that the sum of the points when throwing these cubes on the upwards facing face on landing takes the values 1, 2, ..., 36 with equal probabilities?
There are 25 children in a class. At random, two are chosen. The probability that both children will be boys is \(3/25\). How many girls are in the class?
In the first term of the year Daniel received five grades in mathematics with each of them being on a scale of 1 to 5, and the most common grade among them was a 5 . In this case it turned out that the median of all his grades was 4, and the arithmetic mean was 3.8. What grades could Daniel have?
There are fewer than 30 people in a class. The probability that at random a selected girl is an excellent student is \(3/13\), and the probability that at random a chosen boy is an excellent pupil is \(4/11\). How many excellent students are there in the class?
Three tired cowboys went into a bar, and hung their hats on the buffalo horn at the entrance. When the cowboys left at night, they were unable to distinguish one hat from another and therefore took the three hats at random. Find the likelihood that none of them took their own hat.
A die is thrown over and over again. Let \(P_n\) denote the probability that, at some point, the sum of the points, taken from the numbers that came out on the top face of the die, from all the rolls made, is \(n\). Prove that for \(n \geq 7\) the equality \(P_n = 1/6 (P_{n-1} + P_{n-2} + \dots + P_{n-6})\) is true.
\(A\) and \(B\) shoot in a shooting gallery, but they only have one six-shot revolver with one cartridge. Therefore, they agreed in turn to randomly rotate the drum and shoot. \(A\) goes first. Find the probability that the shot will occur when \(A\) has the revolver.
The probability that a purchased lightbulb will work is 0.95. How many light bulbs should I buy so that, with a probability of 0.99, there would be at least 5 that work among them?
A hunter has two dogs. Once, when he was lost in the woods, he went to the fork in the road. The hunter knows that each of the dogs with probability \(p\) will choose the way home. He decided to release the dogs in turn. If both choose the same road, he will follow them; if they are separated, the hunter will choose the road, by throwing a coin. Will this increase the hunter’s chances of choosing the way home, compared to if he had only one dog?
A marketing company decided to carry out a sociological survey to find out which part of the urban population learns news mostly from radio programs, which part – from TV programs, which part – from the press, and which – from the Internet. For the study, it was decided to use a sample of 2,000 randomly chosen owners of email addresses. Can this sample be considered representative?