Multiple Choice

1. A fair coin is tossed twice. What is the probability of getting exactly one head?

   $\tfrac{1}{2}$

   $\tfrac{1}{8}$

   $\tfrac{3}{4}$

   $\tfrac{1}{4}$

2. A standard six-sided die is rolled twice. What is the probability that both rolls result in an even number?

   $\tfrac{1}{4}$

   $\tfrac{1}{3}$

   $\tfrac{1}{2}$

   $\tfrac{1}{6}$

3. A spinner has 4 equal sections: Red, Blue, Green, Yellow. It is spun twice. What is the probability of landing on Red then Blue?

   $\tfrac{1}{2}$

   $\tfrac{1}{16}$

   $\tfrac{1}{4}$

   $\tfrac{1}{8}$

4. A bag contains 3 red marbles and 2 blue marbles. A marble is drawn, its color noted, and then it is replaced. A second marble is drawn. What is the probability that both marbles drawn are red?

   $\tfrac{9}{25}$

   $\tfrac{3}{5}$

   $\tfrac{1}{5}$

   $\tfrac{6}{25}$

5. A standard deck of 52 cards is used. A card is drawn, replaced, and then a second card is drawn. What is the probability of drawing a King, then an Ace?

   $\tfrac{1}{13}$

   $\tfrac{2}{13}$

   $\tfrac{8}{676}$

   $\tfrac{1}{169}$

6. A bag contains 3 red marbles and 2 blue marbles. A marble is drawn, its color noted, and \emph{not replaced}. A second marble is drawn. What is the probability that both marbles drawn are red?

   $\tfrac{9}{25}$

   $\tfrac{1}{5}$

   $\tfrac{3}{10}$

   $\tfrac{3}{5}$

7. There are 5 boys and 4 girls in a class. Two students are chosen randomly without replacement to represent the class. What is the probability that both students chosen are girls?

   $\tfrac{1}{3}$

   $\tfrac{16}{81}$

   $\tfrac{2}{9}$

   $\tfrac{1}{6}$

8. From a standard deck of 52 cards, two cards are drawn without replacement. What is the probability that both cards are Aces?

   $\tfrac{1}{169}$

   $\tfrac{1}{221}$

   $\tfrac{3}{2652}$

   $\tfrac{1}{13}$

9. A box contains 6 green pens and 4 blue pens. Two pens are selected randomly without replacement. What is the probability that the first pen is green and the second pen is blue?

   $\tfrac{2}{15}$

   $\tfrac{4}{15}$

   $\tfrac{1}{3}$

   $\tfrac{6}{25}$

10. A jar contains 5 red candies and 5 yellow candies. Two candies are picked randomly without replacement. What is the probability that at least one of the candies is red?

    $\tfrac{7}{9}$

    $\tfrac{1}{9}$

    $\tfrac{5}{9}$

    $\tfrac{1}{2}$

11. Two fair six-sided dice are rolled. What is the probability that the sum of the two dice is exactly 7?

    $\tfrac{1}{12}$

    $\tfrac{1}{6}$

    $\tfrac{1}{36}$

    $\tfrac{1}{9}$

12. Two fair six-sided dice are rolled. What is the probability that the product of the two dice is an even number?

    $\tfrac{5}{6}$

    $\tfrac{1}{2}$

    $\tfrac{3}{4}$

    $\tfrac{1}{4}$

13. A fair coin is tossed, and a fair six-sided die is rolled. What is the probability of getting a head on the coin AND an odd number on the die?

    $\tfrac{1}{3}$

    $\tfrac{1}{4}$

    $\tfrac{1}{6}$

    $\tfrac{1}{2}$

14. Given the following table of students:

    $\tfrac{12}{49}$

    $\tfrac{12}{25}$

    $\tfrac{1}{4}$

    $\tfrac{25}{100}$

15. A spinner has sectors labeled 1, 2, 3. It is spun twice. The outcomes are recorded as (first spin, second spin). What is the probability that the sum is greater than 4?

    $\tfrac{1}{9}$

    $\tfrac{4}{9}$

    $\tfrac{2}{9}$

    $\tfrac{1}{3}$

16. A bag contains 4 red balls and 6 blue balls. A ball is drawn, its color noted, and it is replaced. Then a second ball is drawn. What is the probability that the second ball is blue, GIVEN that the first ball was red?

    $\tfrac{1}{2}$

    $\tfrac{4}{10}$

    $\tfrac{3}{5}$

    $\tfrac{2}{5}$

17. A box contains 5 green shirts and 3 yellow shirts. Two shirts are chosen randomly without replacement. What is the probability that the second shirt chosen is yellow, GIVEN that the first shirt chosen was green?

    $\tfrac{3}{7}$

    $\tfrac{3}{8}$

    $\tfrac{1}{3}$

    $\tfrac{5}{8}$

18. Given the following table of owners:

    $\tfrac{20}{60}$

    $\tfrac{35}{60}$

    $\tfrac{15}{35}$

    $\tfrac{4}{7}$

19. A bag contains 4 red, 3 blue, and 3 green marbles. Two marbles are drawn without replacement. What is the probability that the first marble is blue AND the second marble is red?

    $\tfrac{4}{100}$

    $\tfrac{1}{5}$

    $\tfrac{3}{10}$

    $\tfrac{2}{15}$

20. A box contains 7 good batteries and 3 defective batteries. Two batteries are selected randomly \emph{with replacement}. What is the probability that at least one of the selected batteries is good?

    $\tfrac{91}{100}$

    $1 - \left(\tfrac{7}{10}\right)^2$

    $\tfrac{7}{10}$

    $\tfrac{49}{100}$

21. In a basket, there are 6 apples and 4 oranges. Two fruits are picked randomly without replacement. What is the probability that the second fruit picked is an apple?

    $\tfrac{5}{9}$

    $\tfrac{3}{5}$

    $\tfrac{6}{10}$

    $\tfrac{1}{2}$

22. Given the following table of student preferences:

    $\tfrac{50}{80}$

    $\tfrac{30}{80}$

    $\tfrac{3}{7}$

    $\tfrac{40}{70}$

23. A drawer contains 5 black socks and 3 white socks. A person randomly picks two socks one after the other without replacement. What is the probability that they pick two socks of different colors?

    $\tfrac{1}{2}$

    $\tfrac{15}{28}$

    $\tfrac{15}{64}$

    $\tfrac{15}{28}$

24. In a population, the probability of having disease A is $P(A)=0.05$. The probability of having disease B, given that you have disease A, is $P(B\mid A)=0.4$. What is the probability of having both diseases A and B?

    $0.05$

    $0.45$

    $0.02$

    $0.4$

25. A box contains 10 cards numbered 1 to 10. A card is drawn, the number is noted, and the card is \emph{not replaced}. A second card is drawn. What is the probability that the first card drawn was an even number, given that the sum of the two cards drawn is 11?

    $\tfrac{1}{2}$

    $\tfrac{1}{5}$

    $\tfrac{5}{9}$

    $\tfrac{1}{9}$

26. A bag contains $5$ red and $3$ blue marbles. If two marbles are drawn without replacement, the probability that both are red is $\frac{5}{8}\times\frac{X}{7}$. What is the value of $X$?

    $3$

    $4$

    $2$

    $5$

27. A fair coin is flipped twice. If the probability of getting two heads in a row is expressed as $\frac{1}{2}\times\frac{X}{2}$, what is the value of $X$?

    $1$

    $0$

    $2$

    $1/2$

28. A box has $4$ green and $6$ yellow balls. If a ball is drawn and is green, and then a second ball is drawn without replacement, and the probability that the second ball is also green is $\frac{X}{9}$, what is the value of $X$?

    $4$

    $1$

    $6$

    $3$

29. For two events $A$ and $B$, the conditional probability $P(A\mid B)$ is defined as $\dfrac{P(A\cap B)}{P(B)}$, provided that $P(B)$ is not equal to which value?

    $P(A\cap B)$

    $P(A)$

    $0$

    $1$

30. A spinner has $4$ equal sections: red, blue, green, yellow. A fair die is rolled. If the probability of spinning red AND rolling a $6$ is $\dfrac{1}{4}\times\dfrac{X}{6}$, what is the value of $X$?

    $0$

    $6$

    $1$

    $4$

31. When performing a two-step probability experiment without replacement, what happens to the sample space for the second event?

    doubles

    changes

    increases

    stays the same

32. In a school, $60\%$ of students are boys ($B$) and $40\%$ are girls ($G$). $30\%$ of boys like soccer ($S$), and $70\%$ of girls like soccer. If the probability that a randomly chosen student is a girl who likes soccer is $P(G\cap S)=0.40\times X$, what is the value of $X$?

    $1$

    $0.60$

    $0.30$

    $0.70$

33. Given $P(A)=0.5$, $P(B)=0.4$, and $P(A\cap B)=0.2$. What is the conditional probability $P(B\mid A)$?

    $0.4$

    $0.2$

    $0.7$

    $0.5$

34. A standard deck of $52$ cards has $4$ aces. If two cards are drawn without replacement, and the probability of drawing two aces is $\dfrac{4}{52}\times\dfrac{X}{51}$, what is the value of $X$?

    $3$

    $4$

    $1$

    $52$

35. From a bag containing $10$ red and $5$ blue sweets, one sweet is drawn and eaten. If the first sweet was red, there are now $9$ red and $5$ blue sweets left. If the probability of the second sweet being blue is $\dfrac{X}{14}$, what is the value of $X$?

    $15$

    $10$

    $9$

    $5$