Math 3118, Section 3

Spring 2001

Two miscellaneous problems (due Tuesday, January 30)

1. Two cards are drawn at random from a standard deck of 52 cards.
    
   1. How many possible outcomes are there?
      Suggestion: The answer is a binomial coefficient.
      (It's a combination problem, not a permutation problem.)
       
   2. In how many of those outcomes are both of the cards aces?
       
   3. In how many outcomes is there at least one spade?
      Suggestion: It's easier to calculate the number of outcomes leading to the complementary event, i.e. the number of outcomes in which neither card is a spade. So, do this first and then subtract this number from the total number of outcomes.
       
   4. In how many outcomes are both of the cards aces and one of the two is the ace of spades?
      Suggestion: How many choices are there for the "other" ace?
       
       
2. Two cards are drawn at random from a standard deck of 52 cards.
   Use your answers from problem 1 to calculate the following probabilities.
   General method/suggestion: Divide the number of outcomes for the given event by the total number of possible outcomes.
    
   1. What is the probability of drawing two aces?
       
   2. What is the probability of drawing at least one spade?
      Alternative method: If you can find the probability of drawing no spades, you can subtract that result from 1.
       
   3. What is the probability of drawing two aces, one of which is the ace of spades?
       
   4. Are the events "both cards aces" and "at least one spade" independent events?
      Note: You should use methods similar to those in the "solutions" handout.
       

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