Compound Probability of Independent Events

The probabilities of simple events can be combined, or compounded, to find the probability of two or more events happening. When outcomes of these events don't depend on each other, the events are considered independent. This lecture series presents examples of calculating compound probabilities of independent events using diagrams. Watch the videos and complete the interactive exercises.

Practice

The counting principle - Questions

1. Carlos is almost old enough to go to school! Based on where he lives, there are $6$ elementary schools, $3$ middle schools, and $2$ high schools that he has the option of attending.

How many different education paths are available to Carlos? Assume he will attend only one of each type of school.

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2. Bruno is designing his next skateboard. The skateboard store has $2$ types of grip tape, $13$ types of decks, $7$ types of trucks, $4$ types of bearings, and $2$ types of wheels.

How many different skateboards can Bruno create? Assume each skateboard will contain only one type of each component.

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3. John always wears a shirt, pants, socks, and shoes. He owns $12$ pairs of socks, $3$ pairs of shoes, $5$ pairs of pants, and $5$ shirts.

How many different outfits can John make?

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4. Sebastian is going to choose the color, pattern, font, and image for the design of a sweatshirt for his dance team. There are $10$ colors, $4$ patterns, $12$ fonts, and $9$ images for him to choose from. (The printing company charges a fee to add extra design elements, so he will choose only one of each.)

How many different sweatshirt designs are possible?

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