5 mistakes learners make with probability of one event, each one named and explained.
A probability is the ways it can happen out of everything that can happen, and all the possibilities together always make 1.
A dice question about more than 4 is answered 1/6, counting only a single face.
Probability questions usually have one thing happening, so one face is the default picture.
Question. A fair dice, greater than 4
A common answer. 1/6
The answer. 2/6, which is 1/3
Why. Both 5 and 6 are greater than 4, so two faces count.
List the outcomes that satisfy the condition before you write anything down.
Greater than 4 is taken to include the 4, so 4, 5 and 6 are counted.
More than and at least are used interchangeably in ordinary speech.
Question. Greater than 4 on a dice
A common answer. 4, 5 and 6, giving 1/2
The answer. 5 and 6, giving 1/3
Why. Greater than 4 does not include 4 itself.
Underline the comparison word. Greater than excludes; at least includes.
With 5 red, 3 blue and 2 green, blue is given as 3/7, comparing blue against the others.
Odds are quoted that way in everyday life, as three to seven against.
Question. 5 red, 3 blue, 2 green
A common answer. 3/7
The answer. 3/10
Why. There are ten counters in the bag altogether, and the blue ones are among them.
A probability denominator is always everything there is, including what you want.
Three colours in the bag gives an answer of 1/3, whatever the counts are.
Three colours is the most obvious three in the question.
Question. 5 red, 3 blue, 2 green
A common answer. 1/3, one colour out of three
The answer. 3/10
Why. The counters are not equally likely by colour; there are more red than green.
Probability counts equally likely outcomes. Categories are only equally likely if the counts match.
The probability of the event not happening is given where the event itself was asked for.
Both numbers come out of the same calculation and only the last step separates them.
Question. A fair dice, greater than 4
A common answer. 4/6, which is 2/3
The answer. 2/6, which is 1/3
Why. 2/3 is the chance of getting 4 or less, which is the opposite question.
Check your answer against the event you were asked about, not the one you worked out.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.