Mutually and Not Mutually Exclusive Events

Which of the following pairs of events is mutually exclusive?

• Cards: Aces and Spades

• Two dice: Odd and even

• Sit down and stand up

• Sit down and scratch your nose

A card is chosen at random from a pack of 52 playing cards.

What is the probability of a King or a Queen?

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A card is chosen at random from a pack of 52 playing cards.

What is the probability of a King or a Heart?

A number is chosen at random from the set of two-digit numbers from 10 to 99 inclusive.

What is the probability the number contains at least one digit 2?

Two fair dice are thrown.

What is the probability that the score on the first die is 6 or the score on the second die is 5?

There are 30 children in a class and they all have at least one cat or dog.

14 children have a cat, 19 children have a dog.

What is the probability that a child chosen at random from the class has both a cat and a dog?

In a group of 25 boys, 20 play ice hockey, and 17 play baseball. They all play at least one of the games.

What is the probability that a boy chosen at random from the class plays ice hockey but not baseball?

In a class of 29 children, 15 like history and 21 like math. They all like at least one of the two subjects.

What is the probability that a child chosen at random from the class likes math but not history?

In a class of 32 children, 16 have a skateboard, 12 have a bicycle and 17 have a scooter.

5 of them have a skateboard and a bicycle.

7 of them have a skateboard and a scooter.

4 of them have a bicycle and a scooter.

They all have at least one of the three things.

What is the probability that a child chosen at random from the class has a scooter but not a bicycle?

In a class of 35 children, 22 like bananas, 18 like cherries and 13 like strawberries.

7 of them like bananas and cherries.

8 of them like bananas and strawberries.

5 of them like cherries and strawberries.

They all like at least one of the fruits.

What is the probability that a child chosen at random from the class likes cherries only?