Practice Maths

Complementary Events — Solutions

Click any answer to watch the solution video.

  1. Complement rule

    1. P(A) = 0.3:
    2. P(B) = 3/8:
    3. P(C) = 72%:
    4. P(A′) = 0.45:
    5. P(B′) = 5/9:
    6. P(A′) = 15%:
    7. P(A) = 1:
    8. P(A) = 0:

  2. Not-events with dice and cards

    1. P(not a 5):
    2. P(not even):
    3. P(not a factor of 6):
    4. P(not > 4):
    5. P(not a heart):
    6. P(not a king):
    7. P(not a face card):
    8. P(not a red card):

  3. Marbles bag (5 red, 3 blue, 4 green, 8 yellow; total 20)

    1. P(not red):
    2. P(not blue):
    3. P(not yellow):
    4. P(not green):
    5. P(not red and not blue):
    6. P(red or blue):

  4. Mutually exclusive and exhaustive

    1. Getting a 3 and getting a 5:
    2. Even and odd on a die:
    3. Heart and spade:
    4. Red card and black card:
    5. Less than 3 and greater than 4:
    6. Prime and even:

  5. Finding P(A) from conditions

    1. P(yellow):
    2. P(C):
    3. Expected losses in 50 games:
    4. Non-defective out of 500:

  6. Problem solving

    1. Rain forecast 65%:
    2. P(red) = 2/5, 10 blue balls:
    3. Jake’s claim:
    4. True/false quiz, 20 questions:

  7. Sports raffle

    1. (i) P(Mia wins):
    2. (ii) P(Mia does not win):
    3. (iii) P(neither Mia nor Jordan wins):
    4. (iv) Is “Mia wins” the complement of “Jordan wins”?:

  8. Card game strategy

    1. (i) Cards satisfying condition:
    2. (ii) P(club or picture card):
    3. (iii) P(not club and not picture card):

  9. Unknown bag

    1. (i) P(red) and P(blue):
    2. (ii) Numbers in bag (24 marbles):
    3. (iii) New P(red) after adding 6 red marbles:

  10. Medical test

    1. (i) P(negative result for infected person):
    2. (ii) Expected false negatives out of 500:
    3. (iii) Importance in medical testing: