Let W(a:) be the number of 1's in the binary representation of x. For example, W(5) : W(001012) : 2 because there are 2 1's in the binary representation of 5. This is sometimes called the weight of the binary number. A deck of 32 cards has numbers 0 to 3110 written in 5bit binary (000002...111112). 1. 2. What is the probability that the weight of a randomly chosen card is exactiy 3? What is the probability that the weight of the card is 3 and the number on the card is odd, is, P(W = 3 Odd)? . Calculate P(Odd|W = 3], the probability that the card represents an odd number given that the weight of the number is 3. . You are now dealt 3 random cards. What is the expected value for the total weight of your three-card hand? . What is the probability that the total weight of the three cards you were dealt is equal to 13? You may leave your answer as a simple expression