Resources tagged with: Combining probabilities

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Broad Topics > Probability > Combining probabilities

Knock-out

Age 16 to 18 Challenge Level:

Before a knockout tournament with 2^n players I pick two players. What is the probability that they have to play against each other at some point in the tournament?

Put Out

Age 16 to 18 Challenge Level:

After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?

Snooker

Age 16 to 18 Challenge Level:

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

Odd Dice

Age 14 to 16 Short Challenge Level:

These strange dice are rolled. What is the probability that the sum obtained is an odd number?

Dicey Decisions

Age 16 to 18 Challenge Level:

Can you devise a fair scoring system when dice land edge-up or corner-up?

Squash

Age 16 to 18 Challenge Level:

If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?

Do You Brush Your Teeth Every Day?

Age 14 to 18 Challenge Level:

How can we find out answers to questions like this if people often lie?

Voting Paradox

Age 14 to 18 Challenge Level:

Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?

Snooker Frames

Age 16 to 18 Challenge Level:

It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?

Fixing the Odds

Age 14 to 16 Challenge Level:

You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two. . . .

Marbles and Bags

Age 14 to 16 Challenge Level:

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?

Win or Lose?

Age 14 to 16 Challenge Level:

A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. After 2n plays he has won exactly n times. Has. . . .

The Better Bet

Age 14 to 16 Challenge Level:

Here are two games you have to pay to play. Which is the better bet?

Statins and Risk

Age 14 to 16 Challenge Level:

"Statins cut the risks of heart attacks and strokes by 40%"
Should the Professor take statins? Can you help him decide?

How Risky Is My Diet?

Age 11 to 16 Challenge Level:

Newspapers said that eating a bacon sandwich every day raises the risk of bowel cancer by 20%. Should you be concerned?

Taking Chances Extended

Age 14 to 18

This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.

Same Number!

Age 14 to 16 Challenge Level:

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Gambling at Monte Carlo

Age 14 to 16 Challenge Level:

A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?

Molecular Sequencer

Age 14 to 18 Challenge Level:

Investigate the molecular masses in this sequence of molecules and deduce which molecule has been analysed in the mass spectrometer.

Heavy Hydrocarbons

Age 14 to 18 Challenge Level:

Explore the distribution of molecular masses for various hydrocarbons