Math 127A (Practice final exam)December 6, 2010The practice exam has problems. It is about the same length as the actual exam. It does not represent everytype of problem.1. A die is rolled 4 times.(a) Are the rolls independent?(b) Find the probability that all four rolls are a five.(c) Find the chance that at least one roll is a five.(d) Find the probability that at least three fives are rolled.2. Three cards are dealt of the top of a deck. Find the chance that(a) the second card is a queen;(b) all three cards are queens;(c) none of the cards is a queen;(d) not all three cards are queen.3. Four draws will be made from the box12233. Find the chance that a 2 is drawn at leastonce.4. Suppose that there is a 50% chance that a child is male. Of all families that have 4 children, whatproportion have more boys than girls.
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