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Compound Probability Rules

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Compound Probability Rules

Use fractions in simplest form. For each probability, show the rule or calculation you used.

Compound events

A compound event combines two or more simple events.

1.Which option describes a compound event?

Rolling a 4 on one die
Tossing a coin once and getting tails
Rolling two dice and getting a total greater than 9
Picking one blue counter from a bag

2.Select every compound event.

Tossing a coin and getting heads
Picking a yellow sweet and then a green sweet
Rolling a number greater than 4 on a die
Tossing a coin twice and getting tails both times
Choosing a queen or a king from a deck of cards

Independent and dependent events

Independent events do not change one another's probabilities. Dependent events do.

3.If two events are independent, the first event change the probability of the second.

4.If two events are dependent, the first event change the probability of the second.

5.Classify each situation as independent or dependent.

Tossing a coin, then tossing it again
Taking two cards from a pack without putting the first back
Rolling a die and spinning a separate spinner
Taking two counters from a bag without replacing the first
Drawing a card, putting it back, then drawing again

Dependent
Independent
Independent
Independent
Dependent

Multiplication rule

For independent events, multiply the probabilities. For dependent events, update the second probability after the first outcome.

6.A fair six-sided die is rolled twice. Find the probability that both rolls show an odd number. Include the probability for each roll and your multiplication.

7.A standard 52-card pack has 26 red cards, including 6 red face cards. One card is drawn and kept out of the pack. Find the probability that it is red and the next card is a face card. Show both factors in your calculation.

8.A fair spinner has 8 equal sections: 3 are orange, 2 are purple and 3 are teal. It is spun twice. Find the probability of landing on orange first and purple second.

Addition rule and applications

For mutually exclusive events, add their probabilities to find the probability of either event.

9.One card is selected from a standard 52-card pack. Find the probability it is a diamond or a club. Show the addition and simplify your answer.

10.Match each probability rule to its use.

Addition rule
Multiplication rule
Independent events
Dependent events

Find P(A and B) by multiplying probabilities
Find P(A or B) when events cannot happen together
The first outcome alters the next event's probability
The first outcome does not alter the next event's probability

11.A pouch contains 4 black and 5 white counters. Two counters are drawn one after the other without replacement. Calculate the probability that both are black.

12.A box holds 3 lemon sweets and 7 berry sweets. Manaia takes one sweet, eats it, then takes another. Explain why the probability that the second sweet is lemon depends on the first sweet.

Theoretical and experimental probability

Compare what a model predicts with what repeated trials actually produce.

13.Describe a fair method for testing the theoretical probability of getting two odd results when rolling a fair die twice. State what you would record and how many trials you would aim to do.

14.The theoretical chance of two odd results in two rolls of a fair die is 1/4. Give one reason an experiment with 20 trials might produce a different fraction.

15.Plan and record 20 trials of rolling a die twice. For each trial, note the two results and mark whether both are odd. Then calculate the experimental probability.

Trial

First roll

Second roll

Both odd?