# Probability Theory with Coins, Dice and Cards

1. Suppose you have 2 nickels, 3 dimes, and 8 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that

a. You will draw a dime?

b. You will draw a nickel?

c. You will draw a quarter?

2. You are rolling a pair of dice, one red and one green. What is the probability of the following outcomes:

a. The sum of the two numbers you roll from the dice is 9.

b. The sum of the two numbers you roll is 6.

c. The sum of the two numbers you roll is 11.

3. For this question pretend you are drawing cards without replacement from the infamous "Iraq's Most Wanted" deck issued by the U.S. Military before Saddam Hussein and his gang were killed or captured. If you are drawing from the full deck of 52 cards (no jokers), what are the following probabilities:

a. You draw a card that is not Saddam Hussein

b. You draw two cards, which end up being Saddam Hussein and another one with his cousin "Chemical Ali".

c. You draw 14 cards and not one of them is Saddam Hussein [Note: this is a tough one. Please show your work so that even if you didn't get the right answer you can still get partial credit. Grading will be lenient on this one].

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#### Solution Preview

1. Suppose you have 2 nickels, 3 dimes, and 8 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that

2+3+8=13 total outcomes.

a. You will draw a dime? 3/13 = .230769 = 23.77%

b. You will draw a nickel? 2/13 = .153846 = 15.38%

c. You will draw a quarter? 8/13 = .61538 = 61.54%

2. You are rolling a pair of dice, one red and one green. What is the probability of the following outcomes?

There are 11 possible outcomes when rolling two dice (while there is a maximum roll of 12, when rolling two dice you will never get a roll of 1, therefore 11 possible outcomes). We will let r=the Red die and g=the Green ...

#### Solution Summary

Probability theory with coins, dice and cards are examined.

Probability Theory: Examples with coins, dice and 52 cards.

1. Suppose you have 2 nickels, 3 dimes, and 8 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that

a. You will draw a dime?

b. You will draw a nickel?

c. You will draw a quarter?

2. You are rolling a pair of dice, one red and one green. What is the probability of the following outcomes:

a. The sum of the two numbers you roll from the dice is 9.

b. The sum of the two numbers you roll is 6.

c. The sum of the two numbers you roll is 11.

3. For this question pretend you are drawing cards without replacement from the infamous "Iraq's Most Wanted" deck issued by the U.S. Military before Saddam Hussein and his gang were killed or captured. If you are drawing from the full deck of 52 cards (no jokers), what are the following probabilities:

a. You draw a card that is not Saddam Hussein

b. You draw two cards, which end up being Saddam Hussein and another one with his cousin "Chemical Ali".

c. You draw 14 cards and not one of them is Saddam Hussein [Note: this is a tough one. Please show your work.

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