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 school survey found that 60% of students play sports and 40% of students play musical instruments. If playing sports and playing musical instruments are independent events, what percentage of students would you expect to both play sports and play musical instruments?
3. A city survey found that 70% of households have a pet and 40% of households have a garden. The survey also showed that 28% of households have both a pet and a garden. Are having a pet and having a garden independent events for households in this city? Show your reasoning.

…and 4 more problems

1. Tane has a rectangular board divided into a grid of 10 rows and 10 columns, making 100 equal squares. The squares are numbered 1 to 100 row by row, starting from the top left. He randomly selects one square. Let event A be selecting a square with a number that is a multiple of 11. Let event B be selecting a square in the first 4 rows (rows 1–4). Are events A and B independent? Show your reasoning by calculating P(A and B) and comparing it to P(A) * P(B).
2. A school survey found that 60% of students play sports and 40% of students play a musical instrument. If 24% of students do both activities, are playing sports and playing a musical instrument independent events? Show your reasoning.
3. A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If two marbles are drawn at random without replacement, what is the probability that both marbles are red?

…and 4 more problems

1. 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?
2. A box contains 8 red pencils and 4 blue pencils. If two pencils are drawn at random without replacement, what is the probability that both pencils are red?
3. A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If two marbles are drawn without replacement, what is the probability that both are red?

…and 5 more problems