# DHS 18.1 - Option 30. Decisions Ryabushko AP

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Solve the following problems (1 - 6)

1.30. From the numbers 1, 2, 3, ..., 100 are made up every possible pair products. How many numbers obtained will be a multiple of three?

2.30. The store 100 pairs of winter boots one style 10 - brown, and the other - black. Randomly selected 8 pairs of boots. What is the probability that all of the selected Boots - black?

3.30. The probability of failure-free operation in the time T unit included in the device is equal to 0.85. To improve the reliability set a standby unit. Determine the probability of failure of the device for the time T, taking into account the reserve unit.

4.30. Produced shooting at targets three types, of which 5 targets type A, type B 3 target and 3 target type C. The probability of hitting the target of type A is 0.4, in the type of target B - 0.1, the target type C - 0 ,15. Find the probability that: a) the target will be amazed at one shot, if not known, at what type of target it was made; b) in one shot (if you do not know what type of target for it is made) will be hit by the target type A.

5.30. The probability of winning one government bonds equal to 1/3. Find the probability that having 6 bonds of this loan, you can win: a) two bonds; b) for the three bonds; c) not less than two bonds.

6.30. The probability of the birth of a boy is 0.515. Find the likelihood that children born in 1000 boys is not less than 500 but not more than 550.