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Learn about Probability for the 11Plus Exams

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).

11+ Topicwise Probability Article Image 01

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:

11+ Topicwise Probability Article Image 02

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.

11+ Topicwise Probability Article Image 03

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.

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  • Frequently Asked Questions
    What is a good score in 11+ Maths ?

    What counts as a "good" score will vary depending on the school you want to attend. The standardized 11 Plus test score average across the country is roughly 100. The highest average in some areas is 111. The lowest scores would often fall between 60 and 70, while the highest scores would normally fall between 130 and 140. To achieve excellent marks on 11+ Maths Exams, practice 11+ Maths topic-wise questions.

    How to prepare for the 11+ Maths exam?

    The best way to prepare for the 11+ Maths Exam is by practicing 11+ Maths topic-wise questions regularly.

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    What kind of questions are asked in the 11 Plus Maths exam?

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    What do you need to know for the 11 Plus Maths exam?

    The children must master the following topics for the 11 plus exams

    • Number and place value.
    • Addition, subtraction, multiplication, and division.
    • Fractions, percentages, decimals.
    • Ratio and proportion.
    • Algebra.
    • Measurement.
    • Geometry (properties and position of shapes, coordinates)
    • Statistics.

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