# Probability option 1 Deposit fine

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# Description

1. From the cutting of the alphabet laid out the word mathematics. Then, all the letters of the word are mixed and invest in a random order. What is the probability that the word will again MATHEMATICS

2. The two boxes are the same type capacitors. In the first box 20 of capacitors, including 2 faulty. In the second 10, 3 of them faulty. Randomly taken capacitor proved suitable. What is the probability that he was from the first box?

3. Eighteen teams participating in the tournament, divided by lot into two groups of nine teams each. Find the probability that all six leading teams will be distributed into three different groups.

4. Let X - normally distributed random variable with mean 410 and standard deviation 2. Find the probability that X takes a value between 407 and 415.

5. Of the two candidates A and B to an appropriate position, three members of the commission should select one. Everyone can specify either a worthy, or reject both. The applicant is selected when he was found worthy of at least two members of the commission. Find the probability that the recommended A.

6. On average, a fifth of the marketed cars incompleteness. Find the probability that among the ten cars are less than three incompleteness.
7. A random variable X is given the integral function:

Find the values \u200b\u200bof A and B

8. Two automatic machines produced identical products. Given the laws of distribution of the number of defective items produced during the shift on each of them: the first for the second
X:
Xi 0 1 2
Pi 0,1 0,6 0,3
Y:
Yi 0 2
Pi 0,5 0,5
Find the mathematical expectation of the sum of random variables.
9. The machine made some detail. It turns out that the length X is a random variable. When measured in the three cases, the length was equal to 20.1 cm, in the two cases - 19.8 cm, in one case, the length was equal to 20.5 cm, and in four cases - 19.9 cm. Find a lower limit of the probability that the length of the items will be enclosed between 19.7 and 20.3 cm.
10. Of the 10 variants of the control work, written on separate cards, randomly selected and distributed eight eight students, seated on the same row. Find the probability that the serial number will be allocated for this.

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