What does P(A and B) mean in probability?

P(A and B) means the probability that event A and event B both happen. The P stands for probability, and the brackets name the event, so P(heads) = 1/2 for a fair coin. Many books write P(A ∩ B) instead, where the cap-shaped sign ∩ means “and”. Both events together are never more likely than either one alone.

How do you turn a probability into a percentage?

Divide the outcomes you want by all the outcomes, then multiply by 100. If 9 of 20 marbles in a bag are red, the chance of red is 9 ÷ 20 = 0.45, which is 45%. A quicker route is to scale the total up to 100: 20 × 5 = 100, so 9 × 5 = 45, giving 45 out of 100.

Is there an easy way to count outcomes with two dice?

Yes, a 6 by 6 grid makes it easy: write one die’s faces across the top, the other’s down the side, and each sum in its square. Every total then lines up along one diagonal. A total of 9 fills 4 squares, 3 + 6, 4 + 5, 5 + 4 and 6 + 3, so its chance is 4 out of 36, or 1/9.

Why does my child think heads is due after a run of tails?

Your child expects chance to even things out, but a coin has no memory. Each toss starts fresh, with a chance of 1/2 for heads, whatever happened before. Five tails in a row are unlikely before you start, only 1/32, yet once they have happened, the sixth toss is still 1/2. Tossing a coin 50 times together and writing down the results shows how normal streaks are.

Is this probability practice free for a class, and how could a lesson use it?

This chance math game is free for a whole class: its three levels open in any browser, with no pupil accounts and nothing to install. On the board, draw a bag of 20 counters: 5 red, 8 blue and 7 yellow. Pupils write each colour’s chance as a percent, 25%, 40% and 35%, then check that they add up to 100%. Teachers who want each pupil’s progress on one dashboard can add the schools plan, priced per student.

Math practice · reimagined

Probability Game

Dice, coins and marbles fill these probability rounds, yet no answer is a fraction: you type a count, a percent from 0 to 100, or the bottom of 1/? for two combined chances. Chance picks the questions, but the first right answer picks who strikes.

Ages 4–99+ · no download · plays in your browser · 23 languages

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What is probability?

Probability is a number that measures how likely something is, from 0 for impossible to 1 for certain. To find it, count the outcomes you want and divide by all the outcomes that can happen. Pull one marble from a bag of 1 red and 3 blue, and red has a chance of 1 in 4, written 1/4 or 25%.

Every level of Probability

Example: heads on a coin and a 6 on a die

The round shows P(A)=1/2 and P(B)=1/6, like a coin landing heads and a die landing on 6.
The coin cannot change the die, so the two events are independent, and the chance of both is 1/2 × 1/6.
Both tops are 1, so only the bottoms need multiplying: 2 × 6 = 12, and P(A and B) = 1/12.
A coin and a die can land in 12 equally likely pairs, and just one is heads with a 6, so you type 12.

Learn it step by step

Probability starts with counting: out of everything that COULD happen, how many are the outcome you want?

Roll two dice and you can land on 36 different pairs. How many make a total of 7? Count them: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 — that's 6 ways. Seven is the easiest total to roll because it has the most combinations. The whole skill is listing the winners carefully without missing any or counting one twice.

Count every favorable outcome, and type how many there are.

Tips and common mistakes

Every probability lies between 0 and 1, or between 0% and 100%. An answer such as 7/6 or 120% is a sure sign of a counting slip.
A common mistake with two dice is treating 2 + 5 and 5 + 2 as one roll. Picture one die red and one blue: they are two different results.
In a drawer of 3 black and 2 white socks, ask your child the chance of pulling out white without looking: 2 of 5, or 40%. Then test it.

How to play

Rounds ask for the ways two dice can sum to 8, the percent chance when 4 of 5 marbles are red, or the 1/? in P(A and B). Type one whole number on the keypad, with no % sign; 0 is right when no marble is red. Answer before your rival and Tomato strikes, harder for every moment you save.

— Quick answers —

Probability: the short FAQ

What does P(A and B) mean in probability?: P(A and B) means the probability that event A and event B both happen. The P stands for probability, and the brackets name the event, so P(heads) = 1/2 for a fair coin. Many books write P(A ∩ B) instead, where the cap-shaped sign ∩ means “and”. Both events together are never more likely than either one alone.
How do you turn a probability into a percentage?: Divide the outcomes you want by all the outcomes, then multiply by 100. If 9 of 20 marbles in a bag are red, the chance of red is 9 ÷ 20 = 0.45, which is 45%. A quicker route is to scale the total up to 100: 20 × 5 = 100, so 9 × 5 = 45, giving 45 out of 100.
Is there an easy way to count outcomes with two dice?: Yes, a 6 by 6 grid makes it easy: write one die’s faces across the top, the other’s down the side, and each sum in its square. Every total then lines up along one diagonal. A total of 9 fills 4 squares, 3 + 6, 4 + 5, 5 + 4 and 6 + 3, so its chance is 4 out of 36, or 1/9.
Why does my child think heads is due after a run of tails?: Your child expects chance to even things out, but a coin has no memory. Each toss starts fresh, with a chance of 1/2 for heads, whatever happened before. Five tails in a row are unlikely before you start, only 1/32, yet once they have happened, the sixth toss is still 1/2. Tossing a coin 50 times together and writing down the results shows how normal streaks are.
Is this probability practice free for a class, and how could a lesson use it?: This chance math game is free for a whole class: its three levels open in any browser, with no pupil accounts and nothing to install. On the board, draw a bag of 20 counters: 5 red, 8 blue and 7 yellow. Pupils write each colour’s chance as a percent, 25%, 40% and 35%, then check that they add up to 100%. Teachers who want each pupil’s progress on one dashboard can add the schools plan, priced per student.

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