Test: Probability I - Ambitious

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Question 1:   How many four-digit numbers can you get out of 0, 3, 7, 8 ?
18
24
9
30
Question 2:   There are 19 balls in the box: 10 of red ones and 9 of blue ones. In how many ways can two balls of the same color be picked?
9
81
171
162
Question 3:   In how many ways can you pick a captain and his deputy in a group of 23 soldiers?
2 23!
506
2 23 ×100%
253
Question 4:   John has 4 cats. In how many ways he can take 2 of them in his hands (one - in left hand, another - in right)?
2
24
12
8
Question 5:   Three passengers walk into the elevator of the 11 -floor building (ground floor is not included). In how many ways all three passengers can get out on different floors?
165
495
33
990
Question 6:   From the box in which there are 10 white, 4 red and 5 green balls, are randomly picked 3 . What is the probability that all three of them would be white?
0.158
0.3
0.1
0.124
Question 7:   The situation is the same as in the previous task. What is the probability of picking one white, one red and one green ball?
0.158
0.0098
0.034
0.33
Question 8:   At the language school people can only study French, German or both. The event A happens when a random student decides to study French, the event B - when decides to study German. What is the probability when a randomly picked student decides to learn both languages(Event AB ), if P A = 3 4 , P B = 2 5 ?
3 20
1 2
3 10
8 15
Question 9:   There are 2  red and 4 blue balls in the box. Event A happens when the first randomly picked ball is red. Event B happens when second randomly picked ball is also red. Calculate P A B .
1 5
1 3
1 2
1 15
Question 10:   An archer hits the target with the probability 0.9 . What is the probability that out of three shots he hits the target only the third time?
0.003
0.3
0.009
0.001