Iggy's Probability Quiz

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.