Question

1. Determine whether the following events are disjoint.                                                    (3)
   1. Randomly drawing a spade from a deck of cards.

Randomly drawing a heart from a deck of cards.

2. Randomly selecting a person born on January 25.

Randomly selecting a person that is 25 years old.

3. Rolling a 5 on a single roll of a six-sided die.

Rolling an odd number on a single roll of a six-sided die.

Answer 1

1. Randomly drawing a spade from a deck of cards. Randomly drawing a heart from a deck of cards.

In a deck of 52 cards, there are 4 types of cards: Spades, Clubs, Hearts and Diamonds. So a spade can not be a heart and a heart can never be a spade. So these 2 events are disjoint.

2. Randomly selecting a person born on January 25. Randomly selecting a person that is 25 years old. These 2 events are not disjoint because a person born on January 25 can be 25 years old and a person who is 25 years old can have birthday on January 25.

3. Rolling a 5 on a single roll of a six-sided die. Rolling an odd number on a single roll of a six-sided die.

Here the outcome of 2nd event can be 1,3,5 so these 2 events are not disjoint.