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Quiz about Iggys Probability Quiz
Quiz about Iggys Probability Quiz

Iggy's Probability Quiz


I will give a situation such as rolling dice or drawing cards, and ask the probability of a certain thing happening.

A multiple-choice quiz by iggy4. Estimated time: 6 mins.
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Author
iggy4
Time
6 mins
Type
Multiple Choice
Quiz #
261,745
Updated
Jul 23 22
# Qns
10
Difficulty
Difficult
Avg Score
4 / 10
Plays
763
- -
Question 1 of 10
1. There is a carnival game that requires you to roll two standard 6-sided dice. If the sum of the dice rolls is a prime number, then you win. What is the probability of winning? Hint


Question 2 of 10
2. There is a standard 52-card deck. If you draw three cards randomly, without placing each back in the deck, what is the probability that all three cards are spades? Hint


Question 3 of 10
3. A box contains one of each of the bills: $1, $5, $10, $20, $50, and $100. If you randomly draw three bills, then what are the odds that the three bills add to $75? Hint


Question 4 of 10
4. You are running from 3 police officers and there are 5 possible caves to hide in. You hide in a random cave before the officers see you. Each of the officers chooses a random cave to search. More than one officer can search the same cave. If there is a 100% chance a cop will find you if he searches your cave, then what are the odds you will be found? Hint


Question 5 of 10
5. You randomly draw 3 cards from a standard 52-card deck. What are the odds that you draw 3 different suits? Hint


Question 6 of 10
6. A casino game costs $5 to play where you roll two dice. If the sum of the dice rolls is 7, you receive $21 (but not your bet back). If the sum of the dice rolls is not 7, then you lose and get nothing. If you keep playing and stop when you win, what are the odds you will have made money? Hint


Question 7 of 10
7. There is a box containing blue, red, yellow, and green pencils. You randomly draw one of the 50 pencils. You are 2.3 times more likely to draw a green pencil than you are to draw a blue pencil. There are 8 more green pencils than there are red pencils. If you have a 4% chance of drawing a yellow pencil, then what are the odds of drawing a red pencil? Hint


Question 8 of 10
8. You draw two random cards from a standard 52-card deck. What is the probability that you will draw at least one ace? Hint


Question 9 of 10
9. You randomly flip four coins. What is the probability that you will get 2 heads and 2 tails? Hint


Question 10 of 10
10. You randomly roll two dice. What is the probability that the product of the two numbers rolled will equal a square number? Hint



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Quiz Answer Key and Fun Facts
1. There is a carnival game that requires you to roll two standard 6-sided dice. If the sum of the dice rolls is a prime number, then you win. What is the probability of winning?

Answer: 5/12

There are 36 possible results from rolling two dice. The sum of the dice rolls will give you a number from 2 to 12. The prime numbers between them are 2, 3, 5, 7, and 11. The possible dice rolls to get those numbers are: 1-1, 1-2, 2-1, 1-4, 4-1, 2-3, 3-2, 1-6, 6-1, 2-5, 5-2, 4-3, 3-4, 6-5, and 5-6. Since there are 15 results that win the game, the odds of winning are 15/36, or 5/12.
2. There is a standard 52-card deck. If you draw three cards randomly, without placing each back in the deck, what is the probability that all three cards are spades?

Answer: 11 out of 850

The probability of drawing one spade is 13/52 or 1/4. The odds of drawing another spade is 12/51. The odds of drawing a third spade is 11/50. If you multiply (1/4 * 12/51 * 11/50), you get 132/10200. This simplifies to 11/850.
3. A box contains one of each of the bills: $1, $5, $10, $20, $50, and $100. If you randomly draw three bills, then what are the odds that the three bills add to $75?

Answer: 1 in 20

You must draw $20, $5, and $50 since they are the only three bills that total $75. The odds of drawing one of the needed bills is 1/2. The odds of drawing another needed bill is 2/5. The odds of drawing the last needed bill is 1/4. When you multiply the three fractions, you get 2/40 or 1/20.
4. You are running from 3 police officers and there are 5 possible caves to hide in. You hide in a random cave before the officers see you. Each of the officers chooses a random cave to search. More than one officer can search the same cave. If there is a 100% chance a cop will find you if he searches your cave, then what are the odds you will be found?

Answer: 61 out of 125

First I'll figure out the odds that you will not be found. The probability of one cop not finding you is 4/5. The probability of three cops not finding you would be 4/5 * 4/5 * 4/5 = 64/125. This means that 61/125 is the probability that you will be found.
5. You randomly draw 3 cards from a standard 52-card deck. What are the odds that you draw 3 different suits?

Answer: 169/425

There are 4 sets of 13 cards of the same suit, so there is a 39/51 chance that the second card will be a different suit. The probability of the third card being a different suit than the others is only 26/50 or 13/25. When you multiply 39/51 * 26/50 you get 1014/2550, or 169/425.
6. A casino game costs $5 to play where you roll two dice. If the sum of the dice rolls is 7, you receive $21 (but not your bet back). If the sum of the dice rolls is not 7, then you lose and get nothing. If you keep playing and stop when you win, what are the odds you will have made money?

Answer: 671/1296

There are 36 possible results from rolling two dice. Of those results, there are 6 that will give you a 7: 1-6, 6-1, 2-5, 5-2, 4-3, and 3-4. This means there is a 1/6 chance you will roll a 7. To figure the odds of making money, first I'll figure the odds of losing money. You have to lose 4 times in order to lose money.

The odds of losing once are 5/6. If you do 5/6 to the 4th power, you get the odds of losing money, which are 625/1296. This means the odds of making money are 671/1296.
7. There is a box containing blue, red, yellow, and green pencils. You randomly draw one of the 50 pencils. You are 2.3 times more likely to draw a green pencil than you are to draw a blue pencil. There are 8 more green pencils than there are red pencils. If you have a 4% chance of drawing a yellow pencil, then what are the odds of drawing a red pencil?

Answer: 3/10

I will use the first letters of the colors as variables representing the number of pencils of a certain color.
Since you are 2.3 times more likely to draw a green pencil than a blue one, there are 2.3 times more green pencils than blue ones. Since there is a 4% chance of drawing a yellow pencil, there are 2 yellow pencils.
The following equations are true:
B + R + Y + G = 50
B = G/(2.3)
R = G - 8
Y = 2
We can replace the B and R with equal variables in terms of G.
G/(2.3) + G - 8 + 2 + G = 50
Simplified, we get:
G/(2.3) + G + G = 56
Multiply both sides by 2.3 and we get:
G + (2.3)G + (2.3)G = 128.8
Simplified again, we get:
(5.6)G = 128.8
G = 23
Since there are 8 more green pencils than red ones, this means there are 15 red pencils. The odds of drawing a red pencil are 15/50 or 3/10.
8. You draw two random cards from a standard 52-card deck. What is the probability that you will draw at least one ace?

Answer: 33/221

First I'll figure out the odds that you won't draw an ace. Since there are 4 aces, the odds of not drawing an ace are 48/52 or 12/13. The odds of the second card not being an ace are 47/51. Multiply 47/51 by 12/13 and you get 564/663 or 188/221. Since 188/221 are the odds you won't get an ace, the odds you will get at least 1 ace are 33/221.
9. You randomly flip four coins. What is the probability that you will get 2 heads and 2 tails?

Answer: 3/8

There are two possible results of flipping a coin, and 4 coin flips, so the number of possible flip results is 2 to the 4th power or 16. The possible combinations of ways to get two heads and two tails, are: HHTT, HTHT, HTTH, THHT, THTH, and TTHH. Since there are 6 results that are two heads and two tails, the probability of getting that result is 6/16 or 3/8.
10. You randomly roll two dice. What is the probability that the product of the two numbers rolled will equal a square number?

Answer: 2/9

The product of the two numbers rolled will be from 1 to 36. The square numbers between them are 1, 4, 9, 16, 25, and 36.
1-1, 1-4, 4-1, 2-2, 3-3, 4-4, 5-5, and 6-6 are the 8 results you can get that will give you two numbers that will multiply to a square number. There are 36 possible results from rolling two dice, so the odds are 8/36 or 2/9.
Source: Author iggy4

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