Amy's school is 4 miles from her house. Jane lives between Amy's house and the school. After school, Amy walked for 40 minutes at a constant rate to get to Jane's house. The girls stayed at Jane's house for half an hour, then Amy borrowed Jane's bike and rode home at a constant rate. She arrived home 112 hours after school ended.

You are in a room of 22 people (including yourself). each of you has their own deck of 52 cards — assume each deck is well-shuffled, and can be assumed to be fair and independent of each other.1. each you draws the top card of your deck.what is the probability that at least one other person has drawn the same card as you? 2. let x be the number of people who drew a card that was also drawn by at least one other person. for example, if you all drew the same card, x=22, but if you all drew different cards, x=0. what is the expected value of x? 3. consider the same situation as the last question, but this time with 29 people: all 29 of you are in a room with your own decks of cards, and you draw one of them.what is the probability that at least one person draws the ace of spades? 4. let x be the number of the types of card drawn. for example, if everyone draws the same card, x=1, but if everyone draws a different card, x=29. what is the expected value of x?