A box contains 56 balls. The probability of selecting at
random a red ball is five-sevenths. How many balls in the box are not
The event of selecting a red ball
and the event of selecting a ball that is not red are complementary events. The probability of the complement
of 𝐴, denoted 𝐴 bar, is equal to one minus the probability of 𝐴. In this question, we are told that
the probability of selecting a red ball, 𝑃 of 𝑅, is equal to five-sevenths. This means that the probability of
selecting a ball that is not red is one minus five-sevenths. This is equal to two-sevenths. The probability of an event
occurring and its complement must always sum to one.
We are also told in this question
that there are 56 balls in the box. Two-sevenths of these 56 balls are
not red, so we need to calculate two-sevenths of 56. As the word “of” in mathematics
means multiply, we need to multiply two-sevenths by 56. 56 is the same as 56 over one. We can then cross cancel or cross
simplify by dividing 56 and seven by seven. This gives us two over one
multiplied by eight over one, which is equal to 16 over one. We multiply the numerators and
denominators separately. As this is equal to 16, we can
conclude that 16 of the 56 balls in the bag are not red.
An alternative method here would be
to calculate the number of red balls first. We can do this by working out
five-sevenths of 56. This is equal to 40, so we have 40
red balls in the box. This means that the rest of the
balls must not be red. 56 minus 40 is equal to 16. This once again proves that there
are 16 balls in the box that are not red.