Probability: Compound Events

We use probability to tell us how likely something is to occur. Probabilities have values from 0 to 1. A probability of 0 means something is impossible. A probability of 1 means something is certain.

Theoretical probability is a probability that is calculated. For events with equally-likely outcomes, the theoretical probability is the number of ways the event can happen divided by the total number of outcomes in the sample space.

Likelihood increases with larger numbers. 0.5 is greater than 0.2, so it is more likely that your family has apple pie for dessert.

[ggfrac]1/2[/ggfrac] or 50%

[ggfrac]1/6[/ggfrac]

Sample answers: make a table, draw a tree diagram, find the probabilities as single events and then multiply them to find the probability of the compound event

Once you have completed the first event, you need to see how the number of possible outcomes has changed for the second event. You also need to see if the number of favorable outcomes has changed.

Make a table or list to show the outcomes:

H H H

H T H

H H T

H T T

T T T

T H T

T T H

T H H



Only one of these 8 outcomes is H H H, so the probability of getting 3 heads is 18.

or

The probability of getting heads on a toss of a coin is 12. So the probability of getting 3 heads when tossing 3 coins is [ggfrac] 1/2[/ggfrac] × [ggfrac] 1/2[/ggfrac] × [ggfrac] 1/2[/ggfrac], or [ggfrac] 1/8[/ggfrac].

The tree diagram shows the choices of steak and chicken in the top row. Three branches from each main dishes show corn, green beans, and broccoli. Two branches from each vegetable show lemon tart and strawberry ice cream. The tree diagram shows that there are 12 different possibilities for the menu. Only one of those possibilities is chicken, broccoli, and strawberry ice cream. So the probability of having chicken, broccoli, and strawberry ice cream at her dinner party is [ggfrac]1/12[/ggfrac].

There are 6 blue marbles, 4 yellow marbles, and 10 total marbles for the first pick, so the probability of picking a blue marble is [ggfrac]6/10[/ggfrac], or [ggfrac]3/5[/ggfrac]. For the second pick, there are 5 blue marbles, 4 yellow marbles, and 9 total marbles, so the probability of picking a yellow marble for the second pick is [ggfrac]4/9[/ggfrac]. The probability of picking a blue marble on the first pick and a yellow marble on the second pick is [ggfrac]3/5[/ggfrac] × [ggfrac]4/9[/ggfrac] = [ggfrac]12/45[/ggfrac], or [ggfrac]4/15[/ggfrac].