5 mistakes learners make with combined events, each one named and explained.
Independent events multiply along the branches, and taking something out without putting it back changes the bag for the next pick.
Even or greater than 6 on an eight-sided spinner is worked out as 4 plus 2, counting 8 twice.
Adding the two counts is the natural move and the overlap is invisible until you list them.
Question. 1 to 8, even or greater than 6
A common answer. 4 + 2 = 6, so 6/8
The answer. 5/8
Why. The number 8 is both even and greater than 6, so it must only be counted once.
List the outcomes rather than counting them. Repeats then remove themselves.
Two flips are worked out as 1/8, which is the answer for three.
The multiplying rule is remembered without the count of how many times to apply it.
Question. Two flips, both heads
A common answer. 1/2 x 1/2 x 1/2 = 1/8
The answer. 1/2 x 1/2 = 1/4
Why. There are only two flips, so only two halves are multiplied.
Count the events in the question and multiply exactly that many times.
Even or greater than 6 is answered with the even numbers alone.
The first condition is the one you start listing, and the or is easy to lose.
Question. 1 to 8, even or greater than 6
A common answer. 4/8 for the even ones
The answer. 5/8
Why. The 7 satisfies the second condition and is not even.
Or means anything satisfying at least one. Check both lists before counting.
Two heads in two flips is given as 1/2, the probability of one head.
The probability of a head is the fact you know, and it is already a complete answer to something.
Question. Two flips, both heads
A common answer. 1/2
The answer. 1/4
Why. Half the time the first flip already fails, and only half of what is left succeeds again.
Write out all the outcomes for the small cases. The pattern becomes obvious.
Two flips are treated as having three outcomes, two heads, two tails and one of each.
Head and tail really does look like a single result if the order is not tracked.
Question. Two flips
A common answer. three outcomes, so 1/3
The answer. four outcomes, so 1/4
Why. Head then tail and tail then head are two different results.
Outcomes have to be equally likely. One of each happens twice as often as two heads.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.