Independent & Dependent Events

Spinning a spinner, then flipping a coin: ___

Picking a sock from a drawer, then picking another: ___

Rolling a dice three times: ___

Drawing names from a hat without putting them back: ___

Tossing two different coins at the same time: ___

Rolling a red dice and a blue dice: ___

Choosing a prize from a bag, keeping it, then choosing another: ___

Each student spinning a classroom spinner: ___

Picking a card, not replacing it, picking another: ___

Flipping a coin, then rolling a dice: ___

Tossing two separate coins at the same time: ___

Picking raffle tickets without replacement: ___

Spinning a spinner then flipping a coin: ___

Choosing team members one at a time from a group: ___

Two students each rolling their own dice: ___

Give an example of two independent events. Explain why they are independent.

Give an example of two dependent events. Explain why they are dependent.

A bag has 3 red and 2 green balls. You pick one and do NOT put it back. How does this change the next pick?

What if you DID put the ball back? Would the next pick change?

Why does 'without replacement' make events dependent?

Give a real-life example of dependent events (not using marbles or cards).

You pick a red marble and do NOT replace it. How many marbles are left? How many are red?

Is it now more likely or less likely to pick red on the next turn? Why?

What if you picked a blue marble first (without replacing)? How does that change things?

You pick a yellow counter and keep it. How many counters remain? How many are yellow?

What fraction of remaining counters are yellow? What fraction are purple?

Is it now more likely to pick yellow or purple? Explain.

You pick a blue lolly and eat it. How many lollies are left? How many are blue?

What is the new fraction for blue? For red?

If you then eat a red lolly, how does the bag change?

A jar has 5 red, 3 blue and 2 green lollies. You pick one at random and eat it. If you picked red, what is left in the jar?

After eating the red lolly, what is the chance of picking blue next? (How many blue out of how many total?)

Describe an independent events experiment you could do at home:

Describe a dependent events experiment you could do at home:

How would you know the events are independent or dependent from your results?

A bag has 4 red and 6 blue marbles. You pick one red marble. With replacement, P(red) on next pick = ___. Without replacement, P(red) on next pick = ___

Does replacing the marble make the events independent or dependent? Explain.

A coin is flipped twice. Draw or describe the tree diagram. How many possible outcomes?

What is P(two heads)? P(at least one head)?

A dice is rolled and a coin flipped. How many total outcomes are there?

P(heads) = 1/2. P(rolling a 3) = 1/6. P(heads AND rolling a 3) = ___

P(red) = 1/4 (replacing). P(red on second pick) = 1/4. P(two reds) = ___

Does the order of events matter for independent events? Why or why not?

Give two examples of independent events from everyday life.

Give two examples of dependent events from everyday life.

Why does it matter whether events are independent or dependent when calculating probabilities?

Bag: 3 red, 7 blue. You pick red first (not replaced). P(red on 2nd pick) = ___/9

If red had been replaced, P(red on 2nd pick) would be ___/10. Compare these two answers.

You roll a dice and flip a coin. List all possible outcomes (e.g. 1H, 1T, 2H...).

How many outcomes give a number greater than 4 AND tails?

What is P(number > 4 and tails)?

Bag: 2 red, 2 green, 1 yellow. Pick one, do NOT replace. What colours are now possible for the 2nd pick?

If the first pick was red, P(green on 2nd pick) = ___

If the first pick was yellow, P(red on 2nd pick) = ___

A coin is flipped 5 times and lands on heads each time. A student says: 'Tails must be more likely next time.' Is this correct? Explain.

This mistake is called the 'Gambler's Fallacy'. Why do you think people make it?

What is the actual probability of tails on the 6th flip? Explain.