Here’s a question that’s almost guaranteed for Zoho’s first round. Ready for a little brain workout?
A bag contains 3 white, 4 red, and 5 blue balls. Three balls are drawn at random from the bag. What is the probability that all of them are blue?
Please take two minutes to pause and think it through…
Let’s Break It Down Together
First, let’s summarize the problem. The bag contains:
- 3 white balls
- 4 red balls
- 5 blue balls
Adding these up gives us a total of 12 balls in the bag.
Now, we’re looking for the probability that all three balls drawn are blue. To calculate this, we need to:
- Find the total possible outcomes for drawing 3 balls from 12.
- Determine the favorable outcomes where all 3 balls are blue.
Step 1: Total Possible Outcomes
We use combinations to find the total number of ways to choose 3 balls from 12. The formula for combinations is:
C(n, r) = n! / [r!(n — r)!]
Here, n = 12 (total balls) and r = 3 (balls to be drawn). Substituting these values:
C(12, 3) = 12! / (3!(12–3)!) = 220
So, there are 220 possible outcomes for drawing 3 balls from the bag.
Step 2: Favorable Outcomes
Next, we calculate the number of ways to choose 3 blue balls from the 5 available. Again, using the combination formula:
C(5, 3) = 5! / (3!(5–3)!) = 10
So, there are 10 favorable outcomes where all 3 balls are blue.
Step 3: Calculate the Probability
The probability of an event is given by:
P(Event) = Favorable Outcomes / Total Outcomes
Substituting the values:
P(All blue) = 10 / 220 = 1 / 22
Final Answer
The probability that all three balls drawn are blue is 1/22.
Wrap-Up
How did you do? Did you manage to solve it? If not, don’t worry — probability questions like this can be tricky at first, but with practice, they become much easier.
This type of question is common in Zoho’s first-round interviews, so it’s worth mastering the basics of probability and combinations. Who knows — this might just be your ticket to ace the test!
Got more puzzles like this? Share them in the comments and let’s crack them together!
