PHL 215-01

1. If you flip three coins simultaneously, what is the chance of getting at least two heads?

50%
2. W hat is the chance of picking the correct (single) number two times in a row in the standard version of
roulette?
3. Flip three coins. If exactly two of them come up heads, you win $2; otherwise, you lose $1. W hat is the
payoff ratio of this bet?

3/8
4. If the chance of your car crashing in the coming year is .05 and the chance of the hard drive in your
computer crashing in the coming year is .03, what is the chance of both your car and your hard drive
crashing in the coming year?
5. If you roll two dice, what is the chance that each die will come up an even number? (In calculating your
answer, use the formula for the probability of independent events, not the dice table.)

25%
6. Flip two coins. If they both come up heads, you win $3; otherwise, you lose $1. W hat is the payoff ratio of
this bet?
7. In craps, you can make a “proposition bet” that 7 will come up on the next roll of two dice. A $1 bet will
win you $4. What is the payoff ratio of this bet?
8. In craps, you can bet that 2 will come up on the next roll of two dice. A $1 bet will win you $29. What is
the payoff ratio of this bet?

9.  Consider the following game. You and another person each draw one card from a deck; the person who
draws the highest card wins. (The cards, in ascending order of value, are 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K,
A.) If you both draw the same value card, no one wins. Suppose you have drawn a 9, and your opponent is
about to draw. W hat is the chance of your winning the game?

10. Consider the following game. You draw a card from a deck. If you draw a face card (a jack, queen, or
king), you win $3. If you draw some other card, you lose $1. What is the payoff ratio of this bet?

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