### Video Transcript

A bag contains 30 colored
marbles. The probability of choosing a white
marble at random is two-fifths. How many white marbles are in the
bag?

We begin by recalling that the
probability of an event is equal to the number of favorable outcomes divided by the
total number of possible outcomes. This can be written more formally
as shown. π of πΈ is equal to π of πΈ over
π of π, where π is a sample space and π of π is its size, πΈ is the event weβre
interested in, and π of πΈ is its size and π of πΈ is its theoretical
probability.

In this question, the probability
of selecting a white marble is equal to the number of white marbles divided by the
total number of marbles. We are told in the question that
there are 30 marbles in total, and two-fifths of these are white. Letting the number of white marbles
be π₯, we have two-fifths is equal to π₯ over 30. We can multiply both sides of this
equation by 30 such that π₯ is equal to two-fifths multiplied by 30 or two-fifths of
30. As one-fifth of 30 is equal to six,
two-fifths of 30 is 12. We can therefore conclude that
there are 12 white marbles in the bag.

An alternative method would be to
notice that the fractions two-fifths and π₯ over 30 must be equivalent. And since five multiplied by six is
equal to 30 and two multiplied by six is equal to 12, the number of white marbles
must be equal to 12.