​ The probability of selecting a green marble at random form a jar that contains only green, white and yellow marbles is 1/4.

Question

The probability of selecting a green marble at random form a jar that contains only green, white and yellow marbles is \(\frac{1}4\). The probability of selecting a white marble at random form the same jar is \(\frac{1}3 \). If this jar contains 10 yellow marbles. What is the total number of marbles in the jar?

Answer 1

Let the number of green marbles be x and the number of white marbles be y 

Total number of possible outcomes, n(S) = x + y + 10

P(E) = \(\frac{n(E)}{n(S)}\)

Probability of green marbles = \(\frac{1}4\)

⇒ \(\frac{x}{x+y+10}\) = \(\frac{1}4\)

⇒ x + y + 10 = 4x 

⇒ 3x – y – 10 = 0 -------------(i) 

Probability of white marbles = \(\frac{1}3\)

 ⇒ \(\frac{x}{x+y+10}\) = \(\frac{1}3\)

⇒ x – 2y + 10= 0 -------------(ii) 

Solving eq. (i) and (ii), 

we get 

x = 6 and y = 8 

Thus, 

total number of marbles in the jar = x + y + 10 = 6 + 8 + 10 = 24