Question Video: Using Theoretical Probability to Solve a Problem Mathematics • First Year of Preparatory School

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. 𝑃 of 𝐸 is equal to 𝑛 of 𝐸 over 𝑛 of 𝑆, where 𝑆 is a sample space and 𝑛 of 𝑆 is its size, 𝐸 is the event we’re interested in, and 𝑛 of 𝐸 is its size and 𝑃 of 𝐸 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 𝑥, we have two-fifths is equal to 𝑥 over 30. We can multiply both sides of this equation by 30 such that 𝑥 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 𝑥 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.