Probability — Quiz 5

Questions in this quiz (10)

1. As part of a game, Emma rolls a fair six-sided die 4 times. To win the grand prize, the die must show the number 6 on all 4 rolls or the number 1 on all 4 rolls. What is the probability that Emma wins the grand prize?

   • $$0.07%$$
   • $$0.154%$$
   • $$1.54%$$
   • $$15.4%$$

2. Alice randomly selects a card from a pile labeled with integers 2 to 6, and another card from a pile labeled with integers 10 to 16. What is the probability that the product of the numbers on the two cards is odd?

   • $$\frac{6}{35}$$
   • $$\frac{1}{7}$$
   • $$\frac{5}{7}$$
   • $$\frac{3}{7}$$

3. A teacher randomly divides 8 students into 2 groups of 4 students each. If John and Sarah are part of the 8 students, what is the probability that they will be placed in the same group?

   • $$\frac{3}{7}$$
   • $$\frac{2}{35}$$
   • $$\frac{6}{15}$$
   • $$\frac{3}{14}$$

4. A set $$X=\{6,1,-2,-4\}$$ and set $$Y=\{7,4,3,0\}$$. If one number $$x$$ is randomly drawn from set $$X$$ and one number $$y$$ is randomly drawn from set $$Y$$, what is the probability that $$y-x$$ < $$0$$?

   • $$\frac{3}{4}$$
   • $$\frac{1}{2}$$
   • $$\frac{1}{4}$$
   • $$\frac{1}{3}$$

5. A circle is inscribed in a square. The radius of the circle is 2 units. If a point is randomly selected inside the square, what is the probability that the point lies outside the circle but inside the square?

   • $$\frac{\pi-2}{2}$$
   • $$\frac{\pi-2}{4}$$
   • $$\frac{4-\pi}{4}$$
   • $$4-\pi$$

6. Parker enters a charity draw where the chances and corresponding cash prizes are shown in the table below:What is the expected value of Parker’s ticket?

   • $$50$$
   • $$27.30$$
   • $$25.50$$
   • $$7.50$$

7. Alex, Ben, Charlie, and Diana are forming a line for a photo. If Ben is not allowed to stand in the first position, how many different ways can they arrange themselves in the line?

   • $$6$$
   • $$30$$
   • $$24$$
   • $$18$$

8. A multiple-choice question has 5 answers, only one of which is correct. If you guess on 3 such questions, what is the probability you get exactly one correct?

   • $$\frac{77}{125}$$
   • $$\frac{4}{5}$$
   • $$\frac{48}{125}$$
   • $$\frac{16}{25}$$

9. Michelle has a box containing plastic balls. 30% of them are red and the rest are white. Some of the balls have black dots on them. 9% of the balls are red and have black dots on them. If Michelle randomly draws a red ball from the box, what is the probability that it has black dots?

   • $$18%$$
   • $$27%$$
   • $$9%$$
   • $$30%$$

10. How many randomly selected people do you need to have a greater than 50 percent probability that at least one of them was born in December?

    • 5
    • 6
    • 7
    • 8