# Test: Probability I - Normal

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Question 1:   The box fits $\text{\hspace{0.17em}}15\text{\hspace{0.17em}}$ different items:  $7$ pencils and $\text{\hspace{0.17em}}8\text{\hspace{0.17em}}$ pens. $\text{\hspace{0.17em}}3\text{\hspace{0.17em}}$ pencils and $\text{\hspace{0.17em}}5\text{\hspace{0.17em}}$ pens are taken off the box randomly. How many elementary consequences are possible here?
${C}_{7}^{3}×{C}_{8}^{5}$
${C}_{7}^{3}+{C}_{8}^{5}$
${C}_{15}^{8}$
$8!$
Question 2:   During the exam session, professor graded his students' tests. Out of $\text{\hspace{0.17em}}100\text{\hspace{0.17em}}$ students, $\text{\hspace{0.17em}}15\text{\hspace{0.17em}}$ got "A", $\text{\hspace{0.17em}}28\text{\hspace{0.17em}}$ got "B", $\text{\hspace{0.17em}}40\text{\hspace{0.17em}}$ got "C", $\text{\hspace{0.17em}}17\text{\hspace{0.17em}}$ students failed the test. What was the probability $\text{\hspace{0.17em}}p\left(A\right)\text{\hspace{0.17em}}$ not to fail this test?
$0.17$
$0.15$
$0.83$
$0.5$
Question 3:   There are $\text{\hspace{0.17em}}6\text{\hspace{0.17em}}$ blue and $\text{\hspace{0.17em}}9\text{\hspace{0.17em}}$ red pens in the box. What is the least amount of pens you should randomly pick to pick a blue pen with guarantee?
$15$
$6$
$1$
$10$
Question 4:   A group of scientists are providing an experiment on simultaneous tossing of $\text{\hspace{0.17em}}5\text{\hspace{0.17em}}$ coins. The result of the experiment is the final amount of tails that will drop out. How many possible consequences can be at the end of this experiment?
$5$
$10$
$3$
$6$
Question 5:   After some calculations, it was determined that the probability of hitting the target is $\text{\hspace{0.17em}}25%\text{\hspace{0.17em}}$ . Is it possible that after $\text{\hspace{0.17em}}100\text{\hspace{0.17em}}$ shots there will be $\text{\hspace{0.17em}}98\text{\hspace{0.17em}}$ hits?
Yes, only if probability of hitting the target is increased.
Yes
Yes, only if number of hits will increase.
No
Question 6:   Two six-sided dices are being tossed at the same time - blue one and yellow one. What is the probability that the sum of numbers on both dices will be $\text{\hspace{0.17em}}11\text{\hspace{0.17em}}$ ?
$\frac{11}{12}$
$\frac{2}{18}$
$\frac{1}{36}$
$\frac{1}{18}$
Question 7:   In the batch of $\text{\hspace{0.17em}}100\text{\hspace{0.17em}}$ produced bricks, $\text{\hspace{0.17em}}5\text{\hspace{0.17em}}$ are defective. What is the when all $\text{\hspace{0.17em}}8\text{\hspace{0.17em}}$ randomly picked bricks would be non-defective?
$\frac{{C}_{95}^{8}}{{C}_{100}^{8}}$
${C}_{100}^{95}$
${C}_{95}^{8}-{C}_{100}^{8}$
${C}_{95}^{8}$
Question 8:   A basketball player shoots three-pointers with probability of $\text{\hspace{0.17em}}40%\text{\hspace{0.17em}}$ to the basket. What is the probability that he will hit only one time of three shots?
$40%$
$13.33%$
$20%$
$14.4%$
Question 9:   Jack has $\text{\hspace{0.17em}}10\text{\hspace{0.17em}}$ cards and Bill has $\text{\hspace{0.17em}}8\text{\hspace{0.17em}}$ . In how many ways they can exchange $\text{\hspace{0.17em}}2\text{\hspace{0.17em}}$ Jack's cards for $\text{\hspace{0.17em}}2\text{\hspace{0.17em}}$ Bill's cards?
$\text{\hspace{0.17em}}{A}_{18}^{4}$
$\text{\hspace{0.17em}}{C}_{10}^{2}×{C}_{8}^{2}$
$\text{\hspace{0.17em}}{C}_{18}^{4}$
$80$
Question 10:   What is the probability of that the randomly named natural number would be negative?
$0$
$0.5$
$-1$
$1$