The probability of selecting a red ball at random from a jar that contains only red, blue

and orange balls is 1/4. The probability of selecting a blue ball at random from the same

jar 1/3. If the jar contains 10 orange balls, find the total number of balls in the jar.

An excellent question requiring skills in fractions. In fact, fractions should be used in all probability questions whenever possible because they are exact, while decimals represent approximations.

Given:

P (R) = 1/4

P (B) = 1/3

there are only Red (R), Blue (B) and Orange (O) balls in the jar, of which 10 are orange.

Now we know that

P (O) = 1 - 1/4 - 1/3 = 12/12 - 3/12 - 4/12 = 5/12 ... (1)

Let X = total number of balls, then

X*P (O) = 10 ... (given)

substitute (1),

X * (5/12) = 10

solve for X

X = 10 * (12/5) = 24 orange balls.