Algebra in tree and Venn diagrams

12 questions

1. Two events A and B are mutually exclusive. This means that....
2. Sofia has to catch a bus and then a train to get to school. When the bus is late, Sofia is more likely to miss the train and so be late for school. Match each value to its probability.
3. Sofia has to catch a bus and then a train to get to school. When the bus is late, Sofia is more likely to miss the train and so be late for school. P(Sofia is late for school) = ___.
4. Here is a general probability tree. Which of these probabilities give the probability of the highlighted events?
5. One marble is taken at random from a bag of 7 purple and 5 green marbles. The marble is not replaced. A second marble is then taken. The tree diagram shows these two events. Find the value of z.
6. One marble is taken at random from a bag of purple and green marbles. The marble is not replaced. A second marble is then taken. The tree diagram shows the two events. Find P(at least 1 green marble).
7. This probability Venn diagram shows the probability of a random spinner (spun once) landing on a square number or a factor of 36. Which of these probability statements are correct?
8. This probability Venn diagram shows the probability of a random spinner (spun once) landing on a square number or a factor of 36. The value of x is ___. Give your answer as a decimal.
9. Here is a frequency Venn diagram. P(A ∩ B) = 0.2. The total frequency is ___.
10. P(D given C) = 0.4. Which of these equations is correct to find the value of x?
11. A pack of cards contains 30 “character” (c) cards and some “spell” (s) cards. A card is taken at random, replaced and a 2nd card is taken. P(two spell cards) = 0.25. There are ___ cards in the deck.
12. The ratio of cats (c) to dogs (d) in an animal shelter is 4 : 3. Two random animals are taken from the shelter for adoption. Find an expression for P(2 cats).

License: OGL