MA/STAT416: Probability Lecture Notes Spring 2011 1 Chapter 3: Conditional Probability and Independence February 6, 2011 3.4 More on Independence 1. A fair die is rolled twice. Let A be the event that the ﬁrst roll is an even number, and B the event that the sum of the two rolls is an even number. Show that A and B are independent events. 2. Suppose a card is chosen at random from a deck of 52 cards, and let A , B be respectively the events that the card is an ace and that the card is a spade card. Show that A , B are independent events. 3. Suppose a fair die is rolled twice and let A , B be the events that the sum of the two rolls is 7 and that the ﬁrst roll is 1. Show that A,B are independent events. What happens if A is the event that the sum of the two rolls is 8? 4. Jack and his wife Sarah have three cars, and on any given winter morning, they work, independently of each other, with probabilities 0.9, 0.95, and 0.99, respec-tively.
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