Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Question:

A bag contains 6 red balls, 4 green balls and 10 blue balls. Three balls are drawn with replacement. The probability of getting at least 1 green ball is:

Options:

$\frac{1}{4}$

$\frac{61}{125}$

$\frac{1}{2}$

$\frac{29}{57}$

Correct Answer:

$\frac{61}{125}$

Explanation:

The correct answer is Option (2) → $\frac{61}{125}$

Total balls = 6 + 4 + 10 = 20

Probability of green ball = $P(G) = \frac{4}{20} = \frac{1}{5}$

Probability of not green = $P(\text{not G}) = 1 - \frac{1}{5} = \frac{4}{5}$

Three balls drawn with replacement → independent draws

Probability of no green balls in 3 draws = $(\frac{4}{5})^3 = \frac{64}{125}$

Probability of at least 1 green ball = $1 - \frac{64}{125} = \frac{61}{125}$