# Test: Probability I - Ambitious

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Question 1:   How many four-digit numbers can you get out of ?
$18$
$30$
$9$
$24$
Question 2:   There are $\text{\hspace{0.17em}}19\text{\hspace{0.17em}}$ balls in the box: $\text{\hspace{0.17em}}10\text{\hspace{0.17em}}$ of red ones and $\text{\hspace{0.17em}}9\text{\hspace{0.17em}}$ of blue ones. In how many ways can two balls of the same color be picked?
$171$
$81$
$162$
$9$
Question 3:   In how many ways can you pick a captain and his deputy in a group of $\text{\hspace{0.17em}}23\text{\hspace{0.17em}}$ soldiers?
$506$
$\frac{2}{23}×100%$
$\frac{2}{23!}$
$253$
Question 4:   John has $\text{\hspace{0.17em}}4\text{\hspace{0.17em}}$ cats. In how many ways he can take $\text{\hspace{0.17em}}2\text{\hspace{0.17em}}$ of them in his hands (one - in left hand, another - in right)?
$12$
$2$
$8$
$24$
Question 5:   Three passengers walk into the elevator of the $\text{\hspace{0.17em}}11$-floor building (ground floor is not included). In how many ways all three passengers can get out on different floors?
$990$
$495$
$33$
$165$
Question 6:   From the box in which there are $\text{\hspace{0.17em}}10\text{\hspace{0.17em}}$ white, $\text{\hspace{0.17em}}4\text{\hspace{0.17em}}$ red and $\text{\hspace{0.17em}}5\text{\hspace{0.17em}}$ green balls, are randomly picked $\text{\hspace{0.17em}}3\text{\hspace{0.17em}}$ . What is the probability that all three of them would be white?
$0.124$
$0.3$
$0.158$
$0.1$
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?
$0.33$
$0.158$
$0.034$
$0.0098$
Question 8:   At the language school people can only study French, German or both. The event $\text{\hspace{0.17em}}A\text{\hspace{0.17em}}$ happens when a random student decides to study French, the event $\text{\hspace{0.17em}}B\text{\hspace{0.17em}}$ - when decides to study German. What is the probability when a randomly picked student decides to learn both languages(Event $\text{\hspace{0.17em}}A\cap B\text{\hspace{0.17em}}$ ), if ?
$\frac{1}{2}$
$\frac{8}{15}$
$\frac{3}{20}$
$\frac{3}{10}$
Question 9:   There are red and $\text{\hspace{0.17em}}4\text{\hspace{0.17em}}$ blue balls in the box. Event $\text{\hspace{0.17em}}A\text{\hspace{0.17em}}$ happens when the first randomly picked ball is red. Event $\text{\hspace{0.17em}}B\text{\hspace{0.17em}}$ happens when second randomly picked ball is also red. Calculate $\text{\hspace{0.17em}}{P}_{A}\left(B\right)\text{\hspace{0.17em}}$ .
$\frac{1}{15}$
$\frac{1}{2}$
$\frac{1}{5}$
$\frac{1}{3}$
Question 10:   An archer hits the target with the probability $\text{\hspace{0.17em}}0.9\text{\hspace{0.17em}}$. What is the probability that out of three shots he hits the target only the third time?
$0.009$
$0.001$
$0.003$
$0.3$