## Complement of Independent Events are Independent

## Problem 734

Let $E$ and $F$ be independent events. Let $F^c$ be the complement of $F$.

Prove that $E$ and $F^c$ are independent as well.

Add to solve laterLet $E$ and $F$ be independent events. Let $F^c$ be the complement of $F$.

Prove that $E$ and $F^c$ are independent as well.

Add to solve laterSuppose that three fair coins are tossed. Let $H_1$ be the event that the first coin lands heads and let $H_2$ be the event that the second coin lands heads. Also, let $E$ be the event that exactly two coins lands heads in a row.

For each pair of these events, determine whether they are independent or not.

Add to solve laterA card is chosen randomly from a deck of the standard 52 playing cards.

Let $E$ be the event that the selected card is a king and let $F$ be the event that it is a heart.

Prove or disprove that the events $E$ and $F$ are independent.

Add to solve later