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1. Probability in Maths
We come across a lot of terms in our daily life like probably, likely, chances, etc. All these terms point towards probability. Probability is the maths of chance. It has a wide range of daily applications, including forecasting weather, and predicting outcomes when flipping a coin or throwing dice.
What is probability?
Probability is the chance of occurrence of an event. It tells us how much an event is likely to occur. All probabilities are between 0 and 1. If the probability of any event is 0, the event has no chance of happening and the probability of 1 tells us that the event is definitely going to happen.
When the number of possible outcomes is known, we can predict the probability of an event happening with much greater certainty. For example, flipping heads or tails on a coin. With only two possible outcomes (heads or tails), the probability of landing on one or the other is one in two.
1.1. Probability Scale
Probabilities can be written as fractions, decimals or percentages on a scale from 0 to 1 and we can indicate the probability of events by marking it on the probability scale (a number line).
Let’s take a look at some events and probabilities of happening those events.
Impossible: Rolling seven on a fair six-sided dice. Probability is 0.
Unlikely: A race horse winning 25 out of 100 races, the probability of the horse winning is 0.25 or 25%.
Evens: The probability of getting a head when a fair coin is tossed is 0.5 or 50%.
Likely: A race horse winning 75 out of 100 races, the probability of the horse winning is 0.75 or 75%
Certain: The probability of the sun rising in the east is 1 or 100%.
1.2 Finding Probability
When all the outcomes of an event are equally likely (fair spinner, coin or dice), use the following formula to work out the probabilities of such events:
Law of total probability:
If only one possible result can happen at a time, then probabilities of all the results add to 1. For example, a football team can win, lose or draw but these things cannot happen at the same time. So since something must either happen or not happen, then
P(Event happening) + P(Event not happening) = 1
Let us look at the examples below and try to work out the probability.
1.3 Solved Examples
Example: Work out the probability of randomly picking up the letter ‘I’ from the word “PROBABILITY”.
Solution: Letter I is picked up randomly from the word “PROBABILITY”.
The formula is Probability = Number of ways for something to happen ÷ Total number of possible outcomes
Total number of possible outcomes = Number of letters in “PROBABILITY”
= 11
Number of ways of picking up letter ‘I’ = Number of times letter ‘I’ comes in
“PROBABILITY”
= 2
Required probability = 2⁄11
Example: A spinner has different numbers of orange, yellow, red and blue sections.
What is the probability of spinning blue?
Solution: Probabilities of events add up to 1, so to find the probability of the spinner showing blue, add up the remaining probabilities and subtract this from 1.
P(Orange) + P(Yellow) + P(Red) + P(Blue) = 1
0.1 + 0.5 + 0.2 + P(Blue) = 1
P(Blue) = 1 - (0.1 + 0.5 + 0.2)
=1 - 0.8
= 0.2
Probability of spinning blue is 0.2.
