Question

5. a bag contains 8 white balls and some yellow balls. if the probability of drawing a white ball is twice of a yellow ball, then then number of yellow balls in the bag is?

Answer 1

1. P(getting white ball)=8/12=2/3

2. There are 4 yellow balls in the bag.

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Answer 2

Let the number of yellow balls be y.

The total number of balls is therefore :

Total = 8 + y

The probability of getting :

1) White balls = 8/(y + 8)

2) Yellow balls = y/(y + 8)

The probability of drawing a white ball is twice the probability of drawing a yellow ball.

We write this as follows .

8/(y + 8) = 2{y/(y + 8)}

8/(y + 8) = 2y/(y + 8)

8(y + 8) = 2y(y + 8)

8y + 64 = 2y² + 16y

divide through by 2

4y + 32 = y² + 8y

y² + 4y - 32 = 0

The roots of the quadratic equation are + 8 and - 4

doing the substitution we have :

y² - 4y + 8y - 32 = 0

y(y - 4) + 8( y -4) = 0

(y - 4)(y + 8) = 0

y = 4 or -8

we take the positive value.

Hence the number of yellow balls is equal to 4