Two Step Chance Experiments (9)

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.

Tree diagrams basically help you visualise all the different possible combinations of events which can occur.

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

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