Practice section 1 of 8

Which is more likely: getting at least one six in 4 rolls of one die, or getting at least one double six in 24 rolls of two dice?

Let events A and B be the events “scoring no goals” and “scoring 2 goals” in a football match. What is the probability of scoring no goals and 2 goals?

A card is drawn from a full pack of 52 cards. Let A denote drawing an Ace, B drawing a King and C drawing a Spade. Determine whether (a) A and B, (b) B and C, (c) A and C are mutually exclusive. Refer to Example 2 for the deck illustration.

A card is picked at random from a deck of 52 playing cards. Given that it is a spade, find the probability that it is a picture card.

Events A and B satisfy $P(B)=2/3$ and $P(A\mid B)=3/5$. Find $P(A\cap B)$.

The source states that if A and B are independent, then A and B′ are independent. Try proving this result on your own.