Question
Download Solution PDFComprehension
Answer these questions (Qs. 77 - 79) based on the following information.
There are 4 red balls, 4 green balls and 6 blue balls, in a box
If two balls are drawn randomly, what is the probability that at least one of them is blue
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Total Number of Balls:
Red balls: 4
Green balls: 4
Blue balls: 6
Total balls: 4 + 4 + 6 = 14
Total Possible Outcomes (Drawing 2 Balls):
We need to find the number of ways to choose 2 balls out of 14. This is a combination problem.
Total combinations: ¹⁴C₂ = (14 × 13) / (2 × 1) = 91
Finding the Probability of "At Least One Blue" Directly:
It's often easier to find the probability of the opposite event (no blue balls) and subtract it from 1.
Probability of "No Blue Balls":
This means we are choosing 2 balls from the red and green balls only (4 red + 4 green = 8 non-blue balls).
Combinations of non-blue balls: ⁸C₂ = (8 × 7) / (2 × 1) = 28
Probability of no blue balls: 28 / 91 = 4/13
Probability of "At Least One Blue":
Probability (at least one blue) = 1 - Probability (no blue)
Probability (at least one blue) = 1 - (4/13)
Probability (at least one blue) = 9/13
Answer:
The probability that at least one of the two balls drawn is blue is 9/13.
Last updated on Jun 19, 2025
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