IXL | Sample spaces for compound events

Lee picks one marble from a bag and flips this coin one time. The bag has 1 red marble, 1 yellow marble, 1 blue marble, and 1 purple marble.

Which tree diagram represents the sample space of this compound event?

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question

Britney chooses one of these cards and flips this coin one time.

Four cards and a quarter. There is one letter on each card. The letters are L, M, N, and "O."

Which tree diagram represents the sample space of this compound event?

key idea

The sample space of an event is the set of all possible outcomes of the event.

A compound event is made up of two or more simple events.

You can represent the sample space of an event with a tree diagram. Make one branch for each outcome.

solution

This compound event is made of two simple events:

choosing a card and
flipping a coin.

You can represent the sample space of the compound event with a tree diagram.

There are 4 cards: 1 with an L, 1 with an M, 1 with an N, and 1 with an O. So, the first row of the tree diagram will have 4 branches.

The coin has 2 sides: 1 with heads (H) and 1 with tails (T). So, each branch will have 2 more branches.

Notice there are 8 branches on the bottom row of the tree diagram. Each of these branches represents 1 of the 8 equally likely outcomes in the sample space:

choosing the L card and flipping heads
choosing the L card and flipping tails
choosing the M card and flipping heads
choosing the M card and flipping tails
choosing the N card and flipping heads
choosing the N card and flipping tails
choosing the O card and flipping heads
choosing the O card and flipping tails

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II.1Sample spaces of simple events

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