Question

The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is 1/4. The probability of selecting a white marble at random from the same jar is 1/3 . If this jar contains 10 yellow marbles. What is the total number of marbles in the jar?

Answer 1

Let the no. of green marbles = x

The no. of white marbles = y

No. of yellow marbles = 10

Total no. of possible outcomes = x + y + 10 (total no. of marbles)

Probability P(E) = (No.of favorable outcomes)/(Total no.of possible outcomes)

Probability (green marble) = 1/4 = x/(x+y+10)

⇒ x + y + 10 = 4x

⇒ 3x – y – 10 = 0 …..(i)

Probability (white marble) = 1/3 =y /(x+y+10)

⇒ x + y 10 = 3y

⇒ x – 2y + 10 = 0 ….(ii)

⇒ 3x – 6y + 30 = 0 ….(iii)

Multiplying by 3,

Sub (i) from (iii), we get

−6y + y + 30 + 10 = 0

⇒ −5y + 40 = 0

⇒ 5y = 40

⇒ y = 8

Subs. Y in (i), 3x – 8 – 10 = 0

3x – 18 = 0

x = 18/3 = 6

Total no. of marbles in jar = x + y + 10 = 6 + 8 + 10 = 24