The probability of randomly
selecting a rotten apple from a heap of 900 apples is 0.18. What is the number of rotten apples
in the heap?
We have a heap of apples, and we
randomly select one. That means that each apple is
equally likely to be picked. When we’re dealing with equally
likely outcomes, the probability of a given event is a fraction. The denominator of the fraction is
the total number of equally likely outcomes. And the numerator is the number of
those equally likely outcomes that are favourable, that is, that are part of the
In our question, the event is
selecting a rotten apple. And as each apple is equally likely
to be selected, the total number of equally likely outcomes is the total number of
apples. And the number of the favorable
outcomes is the number of these equally likely apples which are rotten. So now what?
Well, we’re told in the question
that the probability of randomly selecting a rotten apple is 0.18. So we substitute this value into
our equation. We’re also told that the total
number of apples in the heap is 900. So we see that 0.18 is the number
of rotten apples over 900. Multiplying both sides of the
equation by 900, we see that 900 times 0.18 is the number of rotten apples that
we’re looking for.
Now we just need to perform this
multiplication, and you can do that in whichever way you’d like. I’m going to use the fact that 900
is nine times 100, and I’m going to give that 100 to the 0.18. 100 times 0.18 is 18. So we have nine times 18, and we
can multiply these in the normal way. Nine times eight is 72. We write the digit zero and then
perform nine times one, to get nine. And then we add 72 and 90. Two plus zero is two, and seven
plus nine is 16. There are therefore 162 rotten
apples in the heap.
You should check that this number
makes sense. 162 is just under a fifth of the
900 apples. And the probability is indeed just
under a fifth. So it seems to be a reasonable