Practice Maths

Comparing Probabilities — Solutions

  1. Theoretical and Experimental Probability

    1. Definition of theoretical probability: Probability calculated from favourable outcomes ÷ total possible outcomes ▶ View Solution
    2. Experimental P(heads) from 20 flips getting 9 heads: 920 ▶ View Solution
    3. Theoretical P(heads): 12 ▶ View Solution
    4. Are they the same? Does this mean the coin is unfair? Not the same, but does not mean the coin is unfair — 20 flips is too few to judge ▶ View Solution
    5. With more trials, does experimental probability get closer or further? Closer to theoretical ▶ View Solution

  2. Likelihood Descriptions

    1. Rolling a 10 on a 6-sided die: Impossible ▶ View Solution
    2. Flipping heads: Equally Likely ▶ View Solution
    3. Drawing a red card from a deck: Equally Likely ▶ View Solution
    4. Rolling a number less than 7: Certain ▶ View Solution
    5. Drawing a blue marble from a bag of 1 blue and 9 other: Unlikely ▶ View Solution

  3. Theoretical Probability — The Lucky Dip

    1. P(green): 12,   0.5 ▶ View Solution
    2. P(yellow): 14,   0.25 ▶ View Solution
    3. P(red): 14,   0.25 ▶ View Solution
    4. P(yellow or red): 12 ▶ View Solution
    5. P(not green): 12 ▶ View Solution

  4. Comparing Probabilities

    1. P(A) = 13 vs P(B) = 25: P(B) is more likely ▶ View Solution
    2. P(C) = 0.6 vs P(D) = 35: They are equal ▶ View Solution
    3. Order 34, 0.6, 70%: 0.6, 70%, 34 ▶ View Solution
    4. Order 13, 0.4, 45%: 13, 0.4, 45% ▶ View Solution
    5. Is 14 > 13? Incorrect — 13 > 14 ▶ View Solution

  5. Experimental Probability — The Tally

    1. Experimental P(red) from 18 reds in 40: 0.45 ▶ View Solution
    2. Experimental P(blue): 0.55 ▶ View Solution
    3. Theoretical P(red): 0.5 ▶ View Solution
    4. Does this suggest the bag is unfair? No — 40 trials is too few to draw a reliable conclusion ▶ View Solution

  6. Probability Number Line

    1. Where does 16 sit on a 0–1 scale? Close to 0 — unlikely ▶ View Solution
    2. Where does 56 sit? Close to 1 — likely ▶ View Solution
    3. Order P(prime on die), P(heart from deck), P(heads): P(heart) = 0.25, then P(prime) = P(heads) = 0.5 ▶ View Solution
    4. Order 0.2, 13, 55%, 34: 0.2, 13, 55%, 34 ▶ View Solution

  7. Dice Challenge

    1. Sample space: {1, 2, 3, 4, 5, 6} ▶ View Solution
    2. P(prime): 12 ▶ View Solution
    3. Experimental P(prime) from 28 primes in 60 rolls: 715 ▶ View Solution
    4. Compare experimental and theoretical: Experimental (0.467) is below theoretical (0.5) ▶ View Solution

  8. Are They Equally Likely?

    1. Bag with 4 red and 6 blue: No — P(red) = 0.4, P(blue) = 0.6 ▶ View Solution
    2. Spinner with unequal sections: No — larger sections are more likely ▶ View Solution
    3. Bag with 5 red and 5 blue — expected red in 100: Yes, equally likely — 50 red balls expected ▶ View Solution
    4. One example each of equal and not equal: Equal: fair die. Not equal: bag with 10 red and 1 blue. ▶ View Solution

  9. Working Backwards from Relative Frequency

    1. Expected wins in 50 games (P = 0.2): 10 wins ▶ View Solution
    2. Does more trials make experimental probability closer or further? Closer to true probability ▶ View Solution
    3. Experimental probability from 95 wins in 500: 0.19 — close to the initial 0.2 ▶ View Solution

  10. The Fête Games

    1. Probabilities for each game: Game A: 16   Game B: 310   Game C: 14 ▶ View Solution
    2. Order least to most likely: Game A, Game C, Game B ▶ View Solution
    3. Expected wins in 60 plays of each: Game A: 10   Game B: 18   Game C: 15 ▶ View Solution