Question
Download Solution PDFA bag contains 4 red and 3 blue balls. If two balls are drawn from this bag at random, what is the probability that they are of different colour?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A bag contains 4 red and 3 blue balls. If two balls are drawn from this bag at random.
Formula used:
The probability of an event = Number of favorable outcomes / Total number of outcomes
Calculation:
- Total number of ways to draw 2 balls out of 7:
\(7C_2 = \frac{7!}{2!(7-2)!} = \frac{7 × 6}{2 × 1} = 21\)
- Number of ways to draw 1 red and 1 blue ball:
- Number of ways to draw 1 red ball out of 4 = \(4C_1 = 4\)
- Number of ways to draw 1 blue ball out of 3 = \(3C_1 = 3\)
Therefore, the number of ways to draw 1 red and 1 blue ball = 4 × 3 = 12
- Hence, the probability that the two balls drawn are of different colors:
Probability = Number of favorable outcomes / Total number of outcomes = 12/21 = 4/7
The probability that the two balls drawn are of different colors is 4/7
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