21. Find the odds for rolling a die and getting a 1.

22. Find the odds for rolling a die and getting an even number.

23. If you pick one card at random from a standard deck of 52 cards, what are the odds it will be an ace?

24. If you pick one card at random from a standard deck of 52 cards, what are the odds it will be a face card?

25. If the probability of a given event is 51 92 , what are the odds against the event happening?

26. If the odds against a given event are 2 to 7, what is the probability of the event occurring?

27. If you pick one card at random from a standard deck of 52 cards, what are the odds it will not be a heart?

28. Find the odds for rolling a die and not getting a 6.

29. A bag contains 3 gold marbles, 6 silver marbles, and 28 black marbles. Someone offers to play this game: You randomly select on marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?

30. A bag contains 2 gold marbles, 10 silver marbles, and 25 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?

31. A friend devises a game that is played by rolling a single six-sided die once. If you roll a 6, he pays you $3; if you roll a 5, he pays you nothing; if you roll a number less than 5, you pay him $1. Compute the expected value for this game. Should you play this game?

32. A company estimates that 0.7% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $350. If they offer a 2 year extended warranty for $48, what is the company's expected value of each warranty sold?

33. An insurance company estimates the probability of an earthquake in the next year to be 0.0013. The average damage done by an earthquake it estimates to be $60,000. If the company offers earthquake insurance for $100, what is their expected value of the policy?

34. A company estimates that 0.9% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $500. If they offer a 2 year extended warranty for $45, what is the company's expected value of each warranty sold?