User contributions
- 16:46, 12 June 2022 (diff | hist) . . (+280) . . N Suppose that we roll two fair 6-sided dice. What is the probability that the two numbers rolled sum to 4? (Created page with "There are 3 ways to roll a sum of 4: 3 on the first die and 1 on the second die, 2 on the first die and 2 on the second die, and 1 on the first die and 3 on the second die. Th...") (current)
- 16:43, 12 June 2022 (diff | hist) . . (+460) . . N Suppose we flip four coins simultaneously: a penny, a nickel, a dime, and a quarter. What is the probability that the penny and dime both come up the same? (Created page with "There are <math>2^4=16</math> possible outcomes, since each of the 4 coins can land 2 different ways (heads or tails). There are 2 possibilities for the penny and the dime: ei...")
- 16:38, 12 June 2022 (diff | hist) . . (+163) . . N Two fair 6-sided dice are rolled. What is the probability the sum rolled is 9? (Created page with "There are 4 different ways to roll a 9 (3+6, 4+5, 5+4, 6+3), which makes the probability of rolling a 9 equal to <math>\dfrac{4}{36} = \boxed{\dfrac{1}{9}}</math>.") (current)
- 16:35, 12 June 2022 (diff | hist) . . (+427) . . N The positive three-digit integer N has a ones digit of 0. What is the probability that N is divisible by 4? Express your answer as a common fraction. (Created page with "An integer is divisible by 4 if and only if a number formed from the last two digits is divisible by 4. If the units digit is 0, all the numbers with even tens digits are divi...")
- 16:33, 12 June 2022 (diff | hist) . . (+381) . . N Steve has one quarter, two nickels and three pennies. Assuming no items are free, for how many different-priced items could Steve individually pay for with exact change? (Created page with "Steve can use no quarters or one quarter, for two possibilities. Steve can use 0, 1, or 2 nickels, for three possibilities. And Steve can use 0, 1, 2, or 3 pennies, for four...")
- 16:27, 12 June 2022 (diff | hist) . . (+939) . . N The perfect squares from $1$ through $2500,$ inclusive, are printed in a sequence of digits $1491625\ldots2500.$ How many digits are in the sequence? (Created page with "We consider it by four cases: <math>\bullet</math> Case 1: There are <math>3</math> perfect squares that only have <math>1</math> digit, <math>1^{2},</math> <math>2^{2},</mat...")
- 16:19, 12 June 2022 (diff | hist) . . (+328) . . N If I have four boxes arranged in a $2 \times 2$ grid, in how many distinct ways can I place the digits $1$, $2$, and $3$ in the boxes, using each digit exactly once, such that each box contains at most one digit? (I only have one of each digit, so one box (Created page with "We can think of placing a <math>0</math> in the fourth box that will necessarily be empty. Now the problem is simple: we have four choices of digits for the first box, three f...")
- 16:15, 12 June 2022 (diff | hist) . . (+223) . . N How many four-digit, positive integers are there where each digit is a prime number? (Created page with "There are four one-digit numbers that are prime: 2, 3, 5, and 7. For each of the four digits of our positive integer, we can choose any one of these four numbers. There are th...")
- 16:12, 12 June 2022 (diff | hist) . . (+242) . . N Joe wants to find all the four-letter words that begin and end with the same letter. How many combinations of letters satisfy this property? (Created page with "There are <math>26</math> choices for the first letter, <math>26</math> for the second, and <math>26</math> for the third. The last letter is determined by the first letter. T...")
