Problem 1 [25 pts (5 pts each)]2 Probability Let W(:z:) 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 3113 written in 5bit binary (000002...111112). 1. What is the probability that the weight of a randomly chosen card is exactly 3? 2. What is the probability that the weight of the card is 3 and the number on the card is odd, i.e.} pay 2 3 0 Odd)? 3. Calculate P( Odd|W = 3), the probability that the card represents an odd number given that the weight of the number is 3