Question

How many red balls should be added to 10red balls in a box containing 50 balls so that the probability becomes 2/3

Answer 1

Given:-

• Initial number of red balls = 10
• Initial number of total balls = 50
• We have to make the probability of drawing a red ball be 2/3

To find:-

• Number of red balls to be added

Answer:-

Let the number of red balls to be added be x.

Then, final number of red balls = (Initial number of red balls) + x = 10 + x

Final number of total balls = (Initial number of total balls) + x = 50 + x

Therefore, after adding x red balls, final probability of drawing a red ball = (Number of favourable events) / (Total number of possible outcomes)

= (10 + x) / (50 + x)

According to the question, this value of the final probability of drawing a red ball becomes 2/3.

So,

(10 + x) / (50 + x) = 2/3

→ 3(10 + x) = 2(50 + x)

→ 30 + 3x = 100 + 2x

→ 3x - 2x = 100 - 30

→ x = 70 Ans

Hence, 70 red balls are to be added.