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Resources tagged with Combining probabilities similar to Semicircle:

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Broad Topics > Probability > Combining probabilities

Snooker Frames

Stage: 5 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?

How Risky Is My Diet?

Stage: 3 and 4 Challenge Level:

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

Statins and Risk

Stage: 4 Challenge Level:

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

The Better Bet

Stage: 4 Challenge Level:

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

Taking Chances Extended

Stage: 4 and 5

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

Same Number!

Stage: 4 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?

Dicey Decisions

Stage: 5 Challenge Level:

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

Lottery Simulator

Stage: 2, 3 and 4 Challenge Level:

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

Marbles and Bags

Stage: 4 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?

Molecular Sequencer

Stage: 4 and 5 Challenge Level:

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

Put Out

Stage: 5 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

Stage: 5 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?

Card Game (a Simple Version of Clock Patience)

Stage: 4 Challenge Level:

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .

Stage: 4 and 5 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?

Gambling at Monte Carlo

Stage: 4 Challenge Level:

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

Knock-out

Stage: 5 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?

Squash

Stage: 5 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?

Fixing the Odds

Stage: 4 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. . . .

Win or Lose?

Stage: 4 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. . . .

Heavy Hydrocarbons

Stage: 4 and 5 Challenge Level:

Explore the distribution of molecular masses for various hydrocarbons