Pick out some outcomes

The idea

An event is any single possible result or combination of results of a random action; an event is a subset of the sample space.

Which ones win?

Two coins are tossed. S = {HH, HT, TH, TT}. You win if at least one coin shows Head. Which outcomes make you win?

How many of the 4 outcomes give at least one Head?

• 2
• 3
• 4

Choose the event

The sample space is given. Tap the outcomes that make the event happen, then Check.

A part of S

An event is any single result or combination of results of a random action. An event is a subset of the sample space.

Two coins, "at least one Head": E = {HH, HT, TH}, a subset of S = {HH, HT, TH, TT}. Die, "greater than 4": E = {5, 6}.

Notes

An event is one result or a combination of results of a random action. It is a subset of the sample space.

Check yourself

A die is rolled. How many outcomes are in the event "the number rolled is greater than 4"?

Answer: 2

Only 5 and 6 are greater than 4, so 2 outcomes: E = {5, 6}.

A die is rolled. How many outcomes are in the event "an even number"?

Answer: 3

E = {2, 4, 6}: 3 outcomes.

Two coins are tossed. Which set is the event "both coins show the same side"?

How is an event related to the sample space?

• {HT, TH}. In HT and TH the two coins show different sides.
• {HH, TT} — correct. Yes. Those are the outcomes with the same side on both coins.
• {HH, HT}. HT has different sides.
• An event is always the whole sample space. That is only one special event.
• An event is a number between 0 and 1. That is a probability, not an event.
• An event is a subset of the sample space — correct. Yes. It is some of the outcomes of S.