4. 1. Definition and example of a random variable. 2. What is the probability of dropping 6 points when throwing a die? 3. How many bouquets of 3 flowers can be made from 2 roses 3 lilies and 3 dahlias? 4. There are 6 balls in an urn: 3 red, 2 blue and 1 white. What is the probability to remove the blue ball after the red. 5. Coin is thrown 5 times. What is the probability of 3 heads? 6. Present the distribution law X for a series of tests in the form of a table when n=3;p(A)=0.2 7. Calculate statistic characteristics (mean median, mode, standard deviation) for data:

1. A random variable is a numerical outcome of a random phenomenon. For example, the roll of a die can result in a random variable that takes on values from 1 to 6.<br />2. The probability of rolling a 6 on a die is 1/6.<br />3. There are 3 roses, 3 lilies, and 3 dahlias, so there are 3! = 6 ways to arrange them in a bouquet of 3 flowers.<br />4. The probability of drawing a blue ball after drawing a red ball is 2/5.<br />5. The probability of getting exactly 3 heads when a coin is tossed 5 times is 5 choose 3 * (1/2)^3 * (1/2)^2 = 10/32 = 5/16.<br />6. The distribution law X for a series of tests with n=3 and p(A)=0.2 is as follows:<br /><br />| X | 0 | 1 | 2 |<br />| --- | --- | --- | --- |<br />| P(X) | 0.512 | 0.384 | 0.064 |<br /><br />7. To calculate the statistic characteristics for the given data, we first need to arrange the data in ascending order: 2, 3, 4, 5, 6. The mean is (2+3+4+5+6)/5 = 4, the median is 4, the mode is none (since all values are unique), and the standard deviation is sqrt(((2-4)^2 + (3-4)^2 + (4-4)^2 + (5-4)^2 + (6-4)^2)/5) = sqrt(10/5) = sqrt(2).