# 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

### 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.

. # Tree Diagrams

### 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.

. # Dependent Events

### 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. # Student Work # ACARA Work Samples # Probability Videos 