Two Step Chance Experiments

List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events (ACMSP225)

LO: To construct a two-step experiment

Know:

  • How to construct an experiment

Understand:

  • that sample spaces can be constructed for two-step experiments

Do:

  • I can construct a sample space for a two-step chance experiment.

 

Independent Events

Independent events are events that are not affected by previous events.

For example, if you flip a coin, it has a probability of 0.5 for landing heads.

To get the probability of landing 2 heads, you just multiply the probability of landing heads twice. (0.5 x 0.5) = 0.25 or 1/4.

To get the probability of landing 3 heads, you just multiply the probability of landing heads three times. (0.5 x 0.5 x 0.5) = 0.125 or 1/8.


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Tree Diagrams

Tree diagrams can also be used to help figure out the probability of events.

If you look at the tree diagram, there is only 1 (HHH) out of a possible 8 outcomes, hence the probability of landing 3 consecutive heads is 1/8.


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Dependent Events

Dependent events are events that are affected by previous events.

For example, if you take a marble out of a bag, the probability changes based on the results of the first result.

The probability of drawing a blue marble in the first instance is 2 out of 5 or (0.4). Now there can be two possible outcomes, you could have drawn a red marble, which would then give you a 2 in 4 chance of drawing a blue marble in the second instance. Or you could have drawn a blue marble in the first instance which would leave you with a 1 in 4 chance of drawing a blue marble in the second instance.


 

Tree Diagrams

Tree diagrams can once again be used to help figure out the probability of events.

What are the chances of drawing 2 blue marbles? There’s a 2/5 chance (0.4) in the first instance, and a 1/4 (0.25) in the second instance. Once again we multiply the probabilities 1/10 (0.1) or 10% chance of drawing 2 blue marbles.


 

Student Work

Probability Videos

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