Estimating Likelihoods

A: Rolling a 6 on a die. B: Flipping heads. C: The sun rising tomorrow. D: Rolling a 1 or 2. Order: ___

Bag has 4 red and 2 blue. Is red or blue more likely? Why?

Spinner A: 2 equal sections. Spinner B: 3 equal sections. On which is red more likely?

Die A: standard (1-6). Die B: only even numbers (2, 4, 6, 2, 4, 6). Which gives a better chance of rolling 6?

Bag A: 3 red, 7 blue. Bag B: 5 red, 5 blue. Which bag gives a better chance of red?

Rolling a 3 on a standard die: ___

Pulling red from 3 red and 7 blue: ___

Flipping heads: ___

Spinning green on a spinner with 5 equal sections (1 green): ___

Rolling an even number: ___

Drawing a vowel from {A, B, C, D, E}: ___

Picking a red ball from 6 red out of 10 total: ___

Rolling a number greater than 4: ___

Describe a game using a coin that is fair (both players have equal chance):

Describe a game using a die that is fair:

Describe an unfair spinner game. Explain who has the advantage and why:

How could you change it to make it fair?

A bag has 3 red and 2 blue marbles. You pick one. What is the probability of red? ___ Blue? ___ Do they add up to 1? ___

Why do all the probabilities for an experiment always add up to 1?

There are 20 marbles: 8 red, 7 blue, 5 green. What is the probability of picking blue? ___ Which colour is most likely?

A spinner has 8 sections: 3 red, 2 blue, 2 yellow, 1 green. What colour is most likely? Least likely?

A: Picking a weekend day randomly. B: A coin lands heads. C: It rains at some point in the next year. D: Rolling a 6. Order: ___

A: Drawing an ace from a deck. B: Drawing a red card. C: Drawing a heart. D: Drawing any card. Order: ___

Spinner A: 1/2 red, 1/2 blue. Spinner B: 3/4 red, 1/4 blue. Which gives a better chance of red?

Bag A: 2 red out of 5. Bag B: 4 red out of 10. Which gives a better chance of red?

Game A: Roll a 6 to win. Game B: Flip heads to win. Which gives a better chance of winning? Why?

Bag A: 7 red, 3 blue. Bag B: 14 red, 6 blue. Is red equally likely in both bags? Explain.

Rolling a number less than 3 on a die: ___

Picking a consonant from {A, B, C, D, E}: ___

Drawing a king from a deck of 52 cards: ___

Rolling a multiple of 3 on a die: ___

Picking a weekend day from the 7 days: ___

Picking blue from 4 blue and 6 red: ___

Rolling an odd number on a die: ___

Picking a face card (J, Q, K) from a deck: ___

Spinning green on a spinner with 8 equal sections (2 green): ___

Design a game using a die where two players have equal chances. Describe the rules:

Design a game using a spinner with 6 equal sections where 3 players have equal chances:

Design a marble game where Player A is twice as likely to win as Player B. How many of each colour?

A spinner has 10 sections. Give each of 3 players different numbers of sections so one has the best chance:

A bag has 5 red, 3 blue, 2 green. P(red) = ___. P(blue) = ___. P(green) = ___. P(red) + P(blue) + P(green) = ___

If you add 5 more red marbles to the bag, how do the probabilities change?

A raffle has 200 tickets. You buy 10. What is your probability of winning? Express as a fraction and percentage.

There are 15 girls and 10 boys in a class. A student is chosen randomly. What is P(girl)? P(boy)?

P(rain) = 3/5. P(no rain) = ___

P(rolling a 6) = 1/6. P(not rolling a 6) = ___

P(picking red) = 7/10. P(not picking red) = ___

P(winning) = 0.25. P(losing) = ___

Rolling a 3 on a die: fraction = ___ decimal ≈ ___ percentage ≈ ___

Flipping heads: fraction = ___ decimal = ___ percentage = ___

Drawing red from 3 red, 7 blue: fraction = ___ decimal = ___ percentage = ___

P(rolling even) ___ P(rolling odd)

P(drawing red from 4/10 red) ___ P(drawing red from 5/10 red)

P(spinning red on 1/4 red spinner) ___ P(spinning red on 2/6 red spinner)

P(picking A from AEIOU) ___ P(picking a vowel from A-E)

Design an experiment where P(win) = 1/4: ___

Design an experiment where P(win) = 3/5: ___

Design an experiment where P(win) = 1: ___

A class raffle has 30 tickets. You buy 5. P(you win) = ___. P(you don't win) = ___.

A bag has 8 green, 4 red and 4 blue marbles. P(green) = ___ P(not green) = ___

If you double the number of all marbles in the bag, do the probabilities change? ___

A die with faces: 1, 1, 2, 3, 4, 5. Is each outcome equally likely? ___. P(rolling 1) = ___.

A spinner with sections of 90°, 90°, 90°, 90°. Is each section equally likely? ___ Why? ___

A spinner shows green on 40% of spins. What fraction of 50 spins would you expect to be green? ___

If you flip a fair coin and get 5 heads in a row, what is P(heads) on the next flip? Explain.

Why is it important to say 'about' when making probability predictions?

P(heads) = 1/2 = ___%

P(rolling less than 3 on a die) = ___ = ___%

P(picking blue from 3 blue, 7 red) = ___ = ___%

P(winning a prize if there are 5 winners from 100 people) = ___%

Where have you seen the word 'likely' or 'unlikely' used in real life?

Weather forecasters say '70% chance of rain.' What does that mean?

Write your own probability sentence for a school event:

Theoretical P(red): ___. Experimental P(red) from the tally above: ___

Are they equal? ___. Why might they differ?

Would 300 draws give a closer match? Why?

Draw the scale from 0 to 1. Mark: impossible (0), unlikely (~0.25), even (0.5), likely (~0.75), certain (1).

Mark these events: Rain in February in Darwin, rolling a 1 on a die, tossing heads.

A bag has 4 red, 3 blue, 2 green, 1 yellow marble. Total: ___. P(red): ___ P(blue): ___ P(not yellow): ___

If you double all marbles: P(red) = ___ Does it change? ___

How many green marbles must you add to make P(green) = 1/4?

A game: roll a die. Win if you roll 1, 2, or 3. Lose if you roll 4, 5, or 6. Fair or unfair? ___. P(win): ___

A spinner: red (50%), blue (25%), green (25%). Player A wins on red, Player B wins on blue or green. Who is favoured? ___

Design a fair game using a die:

A spinner was spun 200 times: Red=72, Blue=56, Green=44, Yellow=28. Estimate P(red): ___ P(yellow): ___

If the spinner had 4 equal sections, expected count per colour: ___. Do results suggest equal sections? ___

If yellow seems under-represented, how might you check if the spinner is biased?

A doctor says a treatment works 70% of the time. What is the probability it doesn't work? ___

If 1 in 100 people has a disease, and you test positive, what other information do you need to know your P(having the disease)?

Why do people buy insurance even when bad events are unlikely?

A hat contains 12 cards: 1-12. P(drawing a multiple of 3) = ___

P(drawing a number greater than 7) = ___

P(drawing an odd prime) = ___

P(drawing a number less than 1) = ___

Mark P(drawing a spade from a standard deck), P(getting two heads in a row), P(rolling a number ≤ 6) on a scale from 0 to 1:

Which of the above events is most likely? ___. Least likely? ___

P(rain today) = 0.6. P(no rain) = ___

P(spinning red) = 3/8. P(not spinning red) = ___

P(choosing a vowel from the letters A-Z) = ___. P(choosing a consonant) = ___

Design an experiment where P(win) = 1/3 using a die: ___

Design an experiment where P(win) = 3/4 using coloured cards: ___

Design an experiment where P(win) = 2/5 using a spinner: ___

In Snakes and Ladders, is the game purely chance or does skill matter? ___

If you roll a die to move, P(moving 6 spaces on one turn): ___

Lotteries: if there are 1,000,000 tickets and you buy 5, P(winning) = ___. Is this a good investment? ___

There are two paths home: Path A has a 20% chance of traffic. Path B has a 35% chance. Which path is better? ___

You have a 70% chance of passing a test if you study vs 30% without study. How much more likely to pass if you study? ___

How does probability help us make better decisions?

A bag has 4 red, 3 blue, 2 green, 1 yellow marble. P(red) = ___. P(not red) = ___

P(green or yellow) = ___. P(neither blue nor green) = ___

If you drew 100 times (replace each time), expected red marbles: ___

P(rolling an even number on a die): fraction=___, decimal=___, percentage=___

P(choosing a vowel from PROBABILITY): fraction=___, decimal≈___, %≈___

P(rain forecast 40%): fraction≈___, decimal=___

Design a marble game where P(player wins) = 0.4 using 10 marbles. How many winning marbles? ___. Colours? ___

Design a spinner where P(win) = 3/8. Draw and label it:

Is this a fair game? What probability makes a game fair? ___

P(drawing the ace of spades from a standard 52-card deck) = ___. Where on the 0-1 scale? ___

P(rolling a number less than 7 on a standard die) = ___. What type of event? ___

Create your own 'impossible', 'unlikely', 'likely', and 'certain' events in a real-life context:

A bag has 5 red and 3 blue marbles. P(red) = ___. P(blue) = ___. Do they sum to 1? ___

A biased coin shows heads 60% of the time. P(tails) = ___

A spinner has sections of 1/4, 1/4, 1/3, and 1/6. Do these probabilities sum to 1? ___

A basketball team wins 7 out of every 10 games. P(winning next game) = ___

A tennis player has a 65% first-serve success rate. P(first serve in) = ___. P(fault) = ___

If a player draws a random card from 10 cards (numbered 1–10) to decide who goes first, is this fair? ___