Question Type 2: Finding the set of outcomes that come under a certain event for a given experiment Exercises

A single fair die is rolled twice. Let $K$ be the event that the sum of the two rolls equals 7. List all outcomes in $K$.

Two fair six-sided dice are rolled. Let $H$ be the event that both dice show the same number (a double). List the outcomes in $H$.

A fair coin is tossed four times. Let $G$ be the event that exactly three tails occur. List the outcomes in $G$.

A standard deck of 52 cards is shuffled and two cards are drawn without replacement. Let $R$ be the event that both cards are aces. List all outcomes in $R$ using unordered pairs.

A bag contains 4 red balls and 3 blue balls. Two balls are drawn without replacement. Let $Q$ be the event that both balls are red. List the outcomes in $Q$ (use ordered pairs of colours).

For the experiment of tossing a fair coin three times, let $E$ be the event that exactly two heads occur. List the set of outcomes in $E$.

A fair die is rolled twice. Let $V$ be the event that neither roll shows a 1. Use set notation to describe the event $V$.

A fair coin and a fair six-sided die are used once each. Let $M$ be the event that the coin shows heads and the die shows an even number. List all outcomes in $M$.

A fair coin is tossed five times. Let $P$ be the event that exactly three heads occur. State the number of outcomes in $P$ and describe the structure of these outcomes.

In an experiment, a coin is tossed and a die is rolled. Let $W$ be the event that the coin shows tail or the die shows a multiple of 3 (or both). List all outcomes in $W$.

Three fair six-sided dice are rolled. Let $N$ be the event that exactly one die shows a 6. Find the number of outcomes in $N$.

A spinner has sectors numbered 1, 2, 3, and 4. It is spun twice. Let $U$ be the event that the sum of the two results is at most 5. List all outcomes in $U$.

A fair coin is tossed three times. Let $F$ be the event that at least two heads occur. Determine the set of outcomes in $F$.