Peter proposes to Sam the opportunity to play the following game. Peter gives Sam two boxes of sweets. In each of the two boxes are chocolate sweets and caramels. In all, there are 25 candies in both boxes. Peter proposes that Sam takes a candy from each box. If both sweets turn out to be chocolate, then Sam wins. Otherwise, Peter wins. The probability that Sam will get two caramels is 0.54. Who has a greater chance of winning?
On each of four cards there is written a natural number. Take two cards at random and add the numbers on them. With equal probability, this amount can be less than 9, equal to 9 or more 9. What numbers can be written on the cards?
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.
\(A\) 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.
Kate and Gina agreed to meet at the underground in the first hour of the afternoon. Kate comes to the meeting place between noon and one o’clock in the afternoon, waits for 10 minutes and then leaves. Gina does the same.
a) What is the probability that they will meet?
b) How will the probability of a meeting change if Gina decides to come earlier than half past twelve, and Kate still decides to come between noon and one o’clock?
c) How will the probability of a meeting change if Gina decides to come at an arbitrary time between 12:00 and 12:50, and Kate still comes between 12:00 and 13:00?
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?