Putting it all Together 1. If two dice are thrown, state the following probabilities. a) Exactly one die shows a four b) Both show four ") The total is six 2. If one card is drawn from a pack of 52 playing cards, calculate the following probabilities. a) The card is an ace D) The card is a black ace c) The card is an ace or a king 3. A committee of 4 is randomly chosen from a group of 25 men and 30 women. Find the following probabilities. a) The committee contains Adam and Steve b) The committee consists of three men and one woman c) The committee consists of at least one women 4. A drawer contains 10 black socks, 6 brown socks, and 3 red white socks, well-mixed. a) If a man opens the drawer in the dark and removes 2 socks, what is the probability that he will get a matched pair? b) If he removes 4 socks, what is the probability that he will get a matched pair? 5. A bag contains 7 red balls and 4 black balls. If 3 balls are drawn at random without replacement, calculate the following probabilities a) All three are red b) All three are black @) Two are red and one is black 6. If 2 cards are drawn from a pack of 52 playing cards without replacement. What are the odds that none of the cards is an ace? 7. Two balls are drawn without replacement from a bag containing 8 red balls and 5 black balls. What are the odds that both balls are red?8. a) How many arrangements of streET are there? Notee and E are distinguishable. b) How many arrangements of street are there? () How many arrangements of the letters adabbed are there? 9. In the arrangement of all the letters of the word OTTAWA, how many a) Start with T, and the second letter is not T? b) Have T and A side by side? 10. How many 5-letter words can be made using the letters of the word BLACKSMITH if a) no restrictions. b) B must be last, C in the middle, and a vowel first