Always happens
A sure event has probability 1.
Less than 7
A fair die is thrown once. Let E be the event getting a number less than 7.
What is P(E)?
What this lesson covers
The idea
An event certain to occur has every possible outcome favourable to it; it is called a sure (or certain) event and its probability is 1.
Less than 7
A fair die is thrown once. Let E be the event getting a number less than 7.
What is P(E)?
- 0
- 1/2
- 1
Light up every face
The dial k decides the event E, "a number less than k". The lit faces are the favourable ones. Turn the dial until every face is favourable.
Every outcome favourable, probability 1
An event that is certain to occur has every possible outcome favourable to it. It is called a sure event (or certain event), and its probability is 1.
Every face of a die shows a number less than 7, so the number of favourable outcomes is 6, the same as the number of all possible outcomes: P = 6/6 = 1. The top of the fraction equals the bottom, so the fraction is 1.
With two dice, every one of the 36 outcomes has a sum of at most 12, so P(sum is at most 12) = 36/36 = 1.
Notes
An event that is certain to occur has every possible outcome favourable. It is a sure event, and P(E) = 1.
Check yourself
A die is thrown once. Find the probability of getting a number less than or equal to 6.
Answer: 1
All 6 faces are favourable: P = 6/6 = 1.
Two dice are thrown together, so there are 36 outcomes. How many outcomes are favourable to the event "the sum of the two numbers is at most 12"?
Answer: 36
Every pair has a sum of at most 12, so all 36 outcomes are favourable and P = 36/36 = 1.
A bag contains only red balls. One ball is drawn at random. What is the probability that it is red?
A die is thrown once. Which event is sure?
- 0. This would mean no ball is red. But every ball is red.
- 1/2. There is no second colour to share the chance with. Every ball is red, so the favourable outcomes are all the possible outcomes.
- 1 — correct. Yes! Every possible outcome is favourable (every ball is red), so the event is sure and P = 1.
- getting a number less than 8 — correct. Yes! All 6 faces show a number less than 8: P = 6/6 = 1.
- getting a number greater than 1. The face 1 is not favourable, so this can fail. P = 5/6.
- getting an even number. The faces 1, 3 and 5 are not favourable, so this can fail. P = 3/6.