# Tag Archives: probability

## Ten-Card Game

A game is played with a deck of ten cards numbered from to . Shuffle the deck thoroughly. Take the top card. If it is numbered , you win. If it is numbered , where , then replace the card … Continue reading

## Second Number Larger Than The First

Suppose a six-sided die has sides numbered through . If a person throws the die two times, what is the probability that the second number will be larger than the first? Source: NCTM Mathematics Teacher, September 2006 Solution The desirable … Continue reading

## Wins and Losses

A person starting with makes eight bets and wins exactly four times. The wins and losses occur in random order. If each wager is for half the money she has at the time of the bet, how much money will … Continue reading

## Same Difference

If fifteen distinct whole numbers are randomly selected from to inclusive, determine the probability that two pairs of these numbers will have the same difference. Source:NCTM Mathematic Teacher, January 2006 Solution What are the possible difference values? There are possible … Continue reading

## Pip Total as Prime Number

A pair of six-sided dice is tossed. What is the probability that the pip total is a prime number? Source: NCTM Mathematics Teacher, January 2006 Solution Number of possible outcomes Desirable outcomes Number of desirable outcomes Probability that the pip … Continue reading

## Ten Different Digits

What is the probability that a number chosen at random from the range to inclusive will contain ten different digits? Round your answer to the nearest millionth. Source: NCTM Mathematics Teacher, January 2006 Solution We divide the large range into … Continue reading

## Tossing Die

Amy, Ben, and Charlie repeatedly take turns tossing a fair die in the given order . What is the probability that Charlie will be the first one to toss a ? Source: NCTM Mathematics Teacher, December 2005 SOLUTION The possible … Continue reading

## Red Face

A cube with all its faces painted red is cut into cubes that are . Some of these new cubes will have some red faces. The cubes are placed in a bag and thoroughly mixed. One is drawn at random … Continue reading

## Black and White Marbles

Each of two boxes contains marbles, and each marble is either black or white. The total number of black marbles is different from the total number of white marbles. One marble is drawn at random from each box. The probability … Continue reading

## Distance Between Two Points

If two points are selected at random from the interval , what is the probability that the distance between them is less than one fourth? Source: NCTM Mathematics Teacher, February 2006 SOLUTION Consider two points and on the interval. Create … Continue reading