# A bag contains 4 white, 7 black and 5 red balls. 4 balls are drawn with replacement. What is the probability that at least two are white?

Given:

Bag contains 4 white, 7 black and 5 red balls

It is told that four balls are drawn with replacement.

We need to find the probability that at least two balls drawn are white.

Let us find the individual probabilities to draw a ball

P(W) = P(drawing a white ball)

P(O) = P(drawing balls other than white)

The possible cases of drawing balls are as shown below:

i. Two whites and two others – 6 cases to draw

ii. Three whites and 1 others – 4 cases to draw

iii. Four whites – 1 case to draw

Since drawing balls are independent events so, the probabilities multiply each other.

The required probability is .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses