Question

A bag contains lettered tiles. The theoretical probability of choosing a vowel is 30%. The bag contains 63 consonants. How many tiles are in the bag?

Answer 1

Theoretical probability is expressed as

Number of favourable outcomes/number of total outcomes

Let x represent the total number of tiles in the bag

Let v represent the number of tiles that are vowels

If there are 63 consonant tiles, then

v + 63 = x

We were told that the theoretical probability of choosing a vowel is 30%. Expressed in decimal,

it is 30/100 = 0.3

This also means that

v/x = 0.3

Substituting x = v + 63 into v/x = 0.3, we have

v/(v + 63) = 0.3

By crossmultiplying,

v = 0.3(v + 63)

v = 0.3v + 18.9

v - 0.3v = 18.9

0.7v = 18.9

v = 18.9/0.7

v = 27

x = 63 + 27 = 90

There are 90 tiles in the bag