Dungeons and Dragons
Fourth of July!
Playing Cards
Coinage
100
You roll a fair four sided die. Each side has three numbers, {1,3,4}, {2,3,4}, {1,2,3}, and {4,1,2}. Whenever a 4 is rolled, your character falls asleep. What is the probability that your character will fall asleep when the die is cast?
What is P(falling asleep)= 3/4....

3 of the sides contain the number 4, making the answer 3/4.
100
You buy 10 packages of 5 bottle rockets to celebrate with on the Fourth of July. These failure rate of these bottle rockets is 1 out of every 15. What is the likelihood of having exactly two duds in your packages of rockets?
What is P(exactly two duds) = 50/225 or 10/45 or 2/9
100
You draw a card from a 52 card deck. What is the probability that you will draw an even numbered card?
What is P(even card) = 20/52

There are 20 even cards total out of the possible 52 card deck.
100
A fair coin is tossed 3 times. What is the probability that you will get at least one head?
What is P(2 heads or less) = 7/8
200
You roll a fair 20-sided die in the game. If you roll an even number below 10, you automatically win. What is the probability that you will not win?
What is P(not winning the game)= 16/20 or 4/5

P(even # below 10) = {2,4,6,8} Total possible numbers (20) - Total numbers below 10 (4)= 16
200
You are having a barbecue at your house and invite 50 of your college friends. 15 of them are studying education, 30 of them are studying history, with an overlap of 5. The rest are studying biology and physics. What is the probability of one of your friends studying both education and history?
What is P(studying history and education)= 5/50 OR 1/10
200
You have a standard 52 card deck and are dealt 5 cards. What is the probability that your hand will consist of only face cards and/or aces?
What is P(all face cards) = 4368/ 2598960 or 1/595

The denominator is all of the 5 hand possibilities (52 choose 5). The numerator is the total number of face cards and aces (16) choose 4, the number of suits.
200
Say you have a weighted coin to toss. Heads appears 60 percent of the time and tails 40%. If you toss this coin 3 times, what is the probability of getting tails each time?
What is P(all tails) 64/1000 or 8/125.

The probability of getting tails off on three tosses is (40/100)^(3)
300
You cast two 20 sided dice in the game. If you get a sum of exactly 20, you will get special powers to win the game. What is the probability that you will get those needed powers?
What is P(sum of exactly 20)= 19/400

There are 19 ways to roll a sum of twenty, and the total number of possible sums is 400.
300
You are going to go on a 3 day vacation. The weather channel forecasts a 50% chance of rain for those 3 days. What is the chance of it not raining at all on your trip?
What is P(not rain)= 1/8

Think of this problem in the same terms as a fair coin being tossed 3 times. There are two options for each day (rain or no rain). The possibility of having no rain for three days is the same as getting all tails or all heads, 1/8.
300
Out of a standard 52 card deck, what is the probability of drawing a black card or odd card?
What is P(black card or odd card) = 36/52 or 18/26 or 9/13

The denominator is the number of all cards to choose from. The numerator is half of the the denominator, as these (black cards or odd cards) represent half of the 52.
300
A fair coin is tossed 5 times. What is the probability of getting less than one head?
What is P(no heads) = 1/32
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