Conditional Probability Worksheets Grade 8

1. Aroha has a spinner divided into 12 equal sections numbered 1 through 12. She spins the spinner once. Event A is 'the number is a multiple of 3' (3, 6, 9, 12). Event B is 'the number is greater than 8' (9, 10, 11, 12). Aroha draws a Venn diagram to show the sample space. Based on the visual diagram, are events A and B independent? Justify your answer by calculating P(A), P(B), P(A and B), and checking the independence condition.
2. A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If you randomly draw one marble, replace it, and then draw a second marble, what is the probability that both marbles drawn are blue?
3. Sophia rolls a fair 6-sided die and flips a fair coin. Event A is rolling an even number. Event B is flipping heads. Are events A and B independent?

…and 4 more problems

1. A rectangular prism has dimensions of 2.5 cm by 4 cm by 6 cm. If you double all three dimensions to create a larger prism, what is the ratio of the surface area of the larger prism to the surface area of the original prism?
2. A rectangular prism is drawn on a coordinate plane with vertices at (0,0,0), (4,0,0), (4,3,0), (0,3,0), (0,0,2), (4,0,2), (4,3,2), and (0,3,2). A smaller prism is created by translating the original prism 1 unit in the positive x-direction and 1 unit in the positive y-direction. What is the volume of the space where the two prisms overlap?
3. A weather station reports that there is a 40% chance of rain on Saturday and a 30% chance of rain on Sunday. If the probability of rain on Sunday is independent of whether it rains on Saturday, what is the probability that it rains on at least one of the two days?

…and 3 more problems

1. P(A) = 1/6, P(B) = 1/6, P(A and B) = 1/36. Are events A and B independent?
2. A school survey found that 60% of students play sports and 40% participate in music. If 24% of students do both activities, what percentage of students play sports but do not participate in music?
3. A school survey found that 60% of students participate in sports and 40% participate in music. If 24% of students participate in both sports and music, are these two activities independent? Show your reasoning.

…and 4 more problems