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.

Explanation:

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.