Maths

Common mistakes in the probability of not happening

4 mistakes learners make with the probability of not happening, each one named and explained.

All common mistakes

Everything that can happen adds to 1, so not happening is 1 minus happening.

A count given where a probability was wanted

What it looks like

The answer is the number of students rather than a fraction or decimal.

Why it happens

The count is the natural first step and it is a satisfying whole number.

A worked example

Question. 30 students, 12 study Spanish

A common answer. 12

The answer. 12/30, which is 2/5

Why. A probability is always between 0 and 1.

Put the two side by side

12 is how many.
2/5 is how likely.

If your probability is bigger than 1, you have given a count.

The complement given as the same number

What it looks like

The probability of not raining is given as 0.35, the same as the probability of raining.

Why it happens

The number in the question is the only number available, so it is the one written down.

A worked example

Question. P(rain) = 0.35

A common answer. P(no rain) = 0.35

The answer. P(no rain) = 0.65

Why. Rain and no rain cannot both be equally likely unless each is 0.5.

Put the two side by side

0.35 and 0.35 add to 0.7.
0.35 and 0.65 add to 1.

The two must add to exactly 1. That is the check, every time.

The other group's probability given

What it looks like

In a class of 30 with 18 studying French, the probability of Spanish is given as 18/30.

Why it happens

The number named in the question is the one that feels like the subject of it.

A worked example

Question. 30 students, 18 study French, the rest Spanish

A common answer. 18/30 for Spanish

The answer. 12/30, which is 2/5

Why. The question asked about the twelve who were never counted directly.

Put the two side by side

18 is the group that was named.
12 is the group that was asked about.

Underline the group in the question. The named number is often the wrong one.

The subtraction from 1 done wrongly

What it looks like

1 minus 0.35 is worked out as 0.55 or 0.75, so the two probabilities do not add to 1.

Why it happens

Subtracting a decimal from a whole number needs the 1 written as 1.00 first.

A worked example

Question. 1 - 0.35

A common answer. 0.55

The answer. 0.65

Why. 0.35 and 0.55 add to 0.9, so one of them must be wrong.

Put the two side by side

0.35 + 0.55 = 0.90.
0.35 + 0.65 = 1.00.

Always add your answer back to the original. Anything other than 1 is a slip.

WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.

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