Question Type 1: Creating sample spaces for different experiments Exercises

Let $E$ be the event that exactly one tail appears when tossing a coin three times. List $E$.

Let $E$ be the event that the last two tosses are the same. List the elements of the set $E$.

Let $E$ be the event that the first toss is a tail in three coin tosses. List the elements of $E$.

Let $E$ be the event that the first and last tosses are the same and there are exactly two heads. List the elements of $E$.

Let $E$ be the event that the total number of heads is odd in three coin tosses. List $E$.

Let $E$ be the event that at least one toss is a head when a fair coin is tossed three times. List $E$.

Express the sample space $S$ of tossing a coin three times using set-builder notation.

Let $E$ be the event that no two heads occur consecutively in three coin tosses. List $E$.

Let $E$ be the event that heads and tails alternate in three tosses (no two adjacent tosses are the same). List the elements of $E$.

Determine the number of elements in the sample space $S$ for three coin tosses.

Let $E$ be the event that exactly two of the three tosses are heads. List the set $E$.

List the sample space $S$ for the experiment of tossing a fair coin three times.