Mutually and Non-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?

• 0

• $\frac{1}{169}$

• $\frac{1}{13}$

• $\frac{2}{13}$

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

What is the probability of a King or a Heart?

• $\frac{1}{52}$

• $\frac{2}{13}$

• $\frac{4}{13}$

• $\frac{17}{52}$

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?

• $\frac{17}{90}$

• $\frac{1}{5}$

• $\frac{17}{100}$

• $\frac{9}{50}$

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?

• $\frac{1}{36}$

• $\frac{11}{36}$

• $\frac{1}{3}$

• $\frac{13}{36}$

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?

• $\frac{1}{10}$

• $\frac{2}{15}$

• $\frac{1}{6}$

• $\frac{1}{5}$

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?

• $\frac{1}{5}$

• $\frac{8}{25}$

• $\frac{12}{25}$

• $\frac{4}{5}$

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?

• $\frac{7}{29}$

• $\frac{14}{29}$

• $\frac{15}{29}$

• $\frac{21}{29}$

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?

• $\frac{9}{32}$

• $\frac{5}{16}$

• $\frac{13}{32}$

• $\frac{1}{2}$

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?

• $\frac{8}{35}$

• $\frac{11}{35}$

• $\frac{13}{35}$

• $\frac{3}{7}$