# Probability 11 option

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1. Three independent experts make a forecast value of the company's shares, while making mistakes with the same probability p. P Find if the likelihood that at least one of them is wrong is 0.488.
2. The amount of electricity consumed by the village during the day, is a random variable whose expectation is 4 th. KWh. Assess the probability that the next day the energy consumption will exceed 8 ths. KWh.
3. Given six cards with the letters H, M, I, I, L, O Find the probability that the word will scrap if one by one randomly selected three cards.
4. Full deck of cards (52 sheets) are divided at random at the bottom of equal parts of 26 cards. Find the probability of the following events, which will be all the aces in one pack.
5. Two hunters simultaneously fire at the target. It is known that the probability of hitting at the first hunter is 0.6, and the second - 0.7. As a result, one of the first volley hit the target. What is the probability that missed the first hunter.

## Additional information

6. Dana integral function of the random variable X

Find the probability that a result of six trials random variable X takes the value twice in the interval of (0, 1).

7. On the market received a large consignment of beef. It is assumed that the weight of the carcass - a random variable subject to the normal distribution with mean a = 800 kg and standard deviation σ = 100 kg. Determine the probability that a randomly selected carcass weight will be between 700 and 900 kg.
8. It is known that on average 60% of the total number of telephone sets produced by the plant is the product of the first grade. What is the probability that the party will be manufactured 120 units of the first grade, if the party contains 200 units?
9. Nefterazvedyvatelnaya company received funding for 10 oil development. The probability of a successful oil exploration 0.1. We assume that oil exploration is carried out independent of each other reconnaissance party. Find the expected number of successful intelligence.
10. The hotel has six single rooms. In these rooms there are 10 candidates: 6 men and 4 women. The hotel follows the rule FIFO: come before served before. All applicants are in the hotel at random. What is the likelihood that the numbers will get four men and two women.

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