Probability problems day 1

Imagine rolling a standard, six-sided die.

1. Write down the sample space of possible outcomes.

2. Let \(A\) be the event that an even number occurs, and \(B\) the event that the result is greater than \(3\). Compute the probabilities \(P(A)\), \(P(B)\), \(P(A \cup B)\), \(P(A \cap B)\), \(P(A^C)\), and \(P(B^C)\).

Consider picking a random card from a standard deck of 52 playing cards. Define the following events:

• \(A\): card is an ace
• \(B\): card has a black suit
• \(D\): card is a diamond
• \(H\): card is a heart

Write the following events in terms of \(A\), \(B\), \(D\), and \(H\):

1. card is an ace of diamonds
2. card is red (the red suits are diamonds and hearts)
3. card is red or an ace
4. card is not a red ace

Run an experiment where you flip a coin 4 times.

1. Write out the sample space of all possible outcomes.
2. What is the probability that you see exactly two heads?