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Probability Basics

Introduction to probability — how likely events are on a scale from 0 to 1.

Last updated: 6 December 2025

★★☆☆☆ Level 2ProbabilitychanceFractions3 min read

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What is Probability?

Probability tells us how likely something is to happen. It is a number between 0 and 1 (or 0% to 100%).

P(event)=number of favourable outcomestotal number of outcomesP(\text{event}) = \dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}
ProbabilityMeaning
0Impossible
0.5Equally likely / unlikely
1Certain

Fair vs. Biased

A fair coin, die, or spinner gives each outcome an equal chance.

Rolling a fair 6-sided die

Total outcomes: 6

P(rolling a 4) =16= \dfrac{1}{6}

P(rolling an even number) =36=12= \dfrac{3}{6} = \dfrac{1}{2}

P(rolling a 7) =0= 0 (impossible)

Complementary Events

The complement of an event is everything that is NOT that event.

P(not A)=1−P(A)P(\text{not A}) = 1 - P(A)

Drawing a red card from a standard deck

P(red) =2652=12= \dfrac{26}{52} = \dfrac{1}{2}

P(not red) =1−12=12= 1 - \dfrac{1}{2} = \dfrac{1}{2}

Experimental Probability

When we run an experiment and count results:

P(event)≈number of times it happenedtotal trialsP(\text{event}) \approx \dfrac{\text{number of times it happened}}{\text{total trials}}

A coin was flipped 100 times and landed heads 58 times.

Experimental P(heads) =58100=0.58= \dfrac{58}{100} = 0.58

The theoretical probability is 0.5. The more trials, the closer results get to 0.5.

Real world: weather forecast

A weather app shows a 70% chance of rain. This means P(rain)=0.7P(\text{rain}) = 0.7, so P(no rain)=1−0.7=0.3P(\text{no rain}) = 1 - 0.7 = 0.3. Forecasters compute these probabilities from thousands of historical weather patterns.

Real world: card games

In a standard deck of 52 cards, P(ace)=452=113≈7.7%P(\text{ace}) = \frac{4}{52} = \frac{1}{13} \approx 7.7\%. Knowing probabilities helps players make better decisions about whether to hold or swap cards.

Real world: medical screening

A screening test for a disease is positive for 1 in every 200 people tested in a healthy population. P(positive)=1200=0.005P(\text{positive}) = \frac{1}{200} = 0.005. Doctors use probability to explain to patients how likely a result is a true positive.

Tip Always check that your probabilities for all possible outcomes add up to exactly 1. If they don't, you have missed an outcome or made an arithmetic error.

Practice Problems

A bag has 3 red, 5 blue, and 2 green marbles. What is the probability of drawing a blue marble?

Show answer
P(blue) = 5/10 = 1/2.

P(rain tomorrow) = 0.3. What is the probability that it will NOT rain?

Show answer
P(no rain) = 1 − 0.3 = 0.7.

A spinner is spun 200 times and lands on red 50 times. What is the experimental probability of red?

Show answer
50/200 = 1/4 = 0.25.