Exploring Compound Probability with Dice

Mr. Maisonette explains a compound probability problem involving rolling a 3 with a green dice and a 5 with a blue dice. He describes how to calculate compound probability by multiplying the probabilities of independent events. A probability matrix is used to illustrate possible outcomes. The video also compares theoretical and experimental probability, showing that actual results can differ from expected outcomes.

What is compound probability?

• The likelihood of an event occurring based on past events

• The likelihood of two independent events happening together

• The total number of possible outcomes in an event

• The probability of an event not happening

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CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

What is the probability of rolling a three with a green dice?

• 1/3

• 1/6

• 1/12

• 1/36

How do you calculate the compound probability of two independent events?

• By multiplying the probabilities of both events

• By dividing the probability of one event by the other

• By subtracting the probabilities of both events

• By adding the probabilities of both events

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CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

What does a probability of 1/36 indicate in this experiment?

• There are 36 dice involved in the experiment

• There is a 36% chance of rolling a three or a five with any dice

• There are 36 different outcomes when rolling one dice

• There is a 1 in 36 chance of rolling a three with the green dice and a five with the blue dice together

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CCSS.HSS.CP.B.7

What is theoretical probability?

• The expected probability of an event occurring based on the total number of outcomes

• The probability of an event not occurring

• The probability of an event occurring based on actual experiments

• The probability of an event occurring once in every experiment

What was the experimental probability of rolling a green three and a blue five?

• 4/36

• 1/9

• 1/6

• 1/36

How many times did the event of rolling a green three and a blue five actually occur in the experiment?

• Four times

• Nine times

• Thirty-six times

• One time

What is the difference between theoretical and experimental probability?

• Theoretical probability is based on the total number of outcomes, while experimental is based on actual experiments

• Experimental probability can only be calculated after the event has occurred

• Theoretical probability is based on actual results, while experimental is not

• There is no difference; they are the same

Why might the experimental probability differ from the theoretical probability?

• Due to calculation errors

• Because of the limited number of trials

• Theoretical probability is always accurate

• Experimental probability does not account for all outcomes

What does the result of the experiment (1/9) suggest about the occurrence of the event compared to the theoretical prediction (1/36)?

• It occurred exactly as expected

• It occurred less frequently than expected

• It occurred more frequently than expected

• The result was inconclusive