____
Maths (Higher)
Conditional probability

Starter quiz

  • Two events A and B are mutually exclusive. This means that....
    • P(A ∩ B) = 0  ✓
    • P(A ∪ B) = 0
    • P(A) + P(B) = 0
    • P(A | B) = 0  ✓
    • P(A | B') = 0
  • 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.
    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.
    • x
      ⇔
      0.05 ✓
    • y
      ⇔
      0.2 ✓
    • z
      ⇔
      0.9 ✓
  • 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) = <span class="blank">______</span>.
    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) = ______.
    • '0.195' ✓
  • Here is a general probability tree. Which of these probabilities give the probability of the highlighted events?
    Here is a general probability tree. Which of these probabilities give the probability of the highlighted events?
    • P(A' ∪ C')
    • P(A' ∩ C')  ✓
    • P(A') × P(C' | A)
    • P(A') × P(C' | A')  ✓
    • P(A') × P(A' | C')
  • 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 <Math>z</Math>.
    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.
    • 7 \over 12
    • 5 \over 12
    • 7 \over 11  ✓
    • 6 \over 11
    • 5 \over 11
  • 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).
    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).
    • \frac{35}{132}
    • \frac{35}{132}
    • \frac{95}{144}
    • \frac{15}{22}  ✓
    • \frac{5}{33}
+