Exercises for Homework 1

1.11. A die is tossed. Find the probability that the upper side of the die shows:

a) six aces; b) an odd number of aces; c) no less than four aces; d) no more than two aces.

1.12. An urn contains 12 balls: 3 white, 4 black and 5 red. Find the probability that a randomly taken ball will be black.

1.13. The first box contains 5 balls with numbers from 1 up to 5, and the second – 5 balls with numbers from 6 up to 10. It has been randomly extracted on one ball from each box. Find the probability that the sum of numbers of the extracted balls will be: 1) no less than 7; 2) equal to 11; 3) no more than 11.

The answer: 2) 0,2; 3) 0,6.

1.14. The relative frequency of workers of an enterprise having a higher education is equal to 0,18. Determine the number of workers having a higher education if the total number of workers of the enterprise is 350.

1.15. 78 seeds have germinated of 100 planted seeds. Find the relative frequency of germination of seeds (seed – семя; to germinate – прорастать).

1.16. Two dice are tossed. Find the probability that: a) the sum of aces equals 5, and the product equals 6;

b) the product of aces doesn’t exceed 6; c) the product of aces is divided on 6.

1.17. A point C is randomly appeared in a segment AB of the length 3. Determine the probability that the distance between C and B exceeds 1. The answer: 2/3.

1.18. A point is randomly thrown inside of a circle of the radius R. Find the probability that the point will be inside the square entered in the circle. It is supposed that the probability of hit of a point in the square is proportional to its area and does not depend on its location regarding the circle. The answer: 2/.

1.19. A coin is tossed twice. Find the probability that the coin lands on heads in both times.

The answer: 1/4.

1.20. A point B(x) is randomly put in a segment OA of the length 6 of the numeric axis Ox. Find the probability that both the segments OB and BA have the length which is greater than 2. The answer: 1/3.