Events that can/can't happen with others
Is it possible?
When we think of things happening, we know some things can't occur at the same time. You can't be sleeping at the same time as you are awake. If you are standing up, you are not sitting down.
Then there are things that may happen at the same time. You might be standing up, or you might be eating. It's also possible that you are standing up and eating!
From the three arrows below, is it possible to choose an arrow that is straight and green?
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While we can choose a green arrow and we can choose a straight arrow, we cannot choose one that satisfies both options. The only straight arrow is red. The only green arrow is curved. Therefore, none of the options satisfies both conditions we were looking for.
Only two outcomes
Sometimes there are only two possibilities that could occur. If you think of tossing a coin, we can only toss a head or a tail. If we only have one coin, there are no other options that could occur at the same time.
In our first video, we will look at events where there can only be two possibilities.
More than two outcomes
Sometimes, such as when you throw a die, you have more things that could happen. A die has $6$6 sides. If we only have one die, then we can only roll a $1,2,3,4,5$1,2,3,4,5 or $6$6. We can't roll a $12$12, as we only have one die.
A deck of cards has $52$52 cards. Within a deck of cards, there are different colours, numbers and patterns. This means there are many possibilities of things that could happen. In the second video, we look at having different options, to see what is possible.
Worked Examples
QUESTION 1
Is it possible for the following two events to happen at the same time?
1) It is a Friday
2) It is raining
Yes
ANo
B
QUESTION 2
A die is rolled.
Is it possible for the following two outcomes to happen at the same time?
1) Rolling a $6$6
2) Rolling an odd number
Yes
ANo
B
QUESTION 3
A dog is randomly selected from the group of dogs shown.
Ten cartoon dogs of various breeds and colors are depicted in different poses. Starting from the top left, the first dog is golden in a neutral standing position with a playful expression. Next to it, is also golden holding a blue ball in a seated position. And the top rightmost, is also a golden dog running with its mouth holding a stick.
Moving down, a black and brown dog with a prominent ruff and alert stance, is followed by a slender brown dog standing. Completing the mid row is a dog resembling a German Shepherd in a standing profile.
In the bottom row, the first dog on the left is brown and white, standing with a broad chest. Adjacent is a standing grey and white dog with a thick, curled tail with its tongue out. Next, there's a shaggy beige dog in a neutral standing position. The final dog on the right end of the bottom row has a distinct black and white spots, also in a neutral standing position.
Which two of these outcomes can occur at the same time?
Selecting a dog that is running
ASelecting a dog with something in its mouth
BSelecting a dog with spots
CSelecting a dog with its tongue out
D