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Two balls are drawn at random from a bag containing 3 white, 3 red, 4 green and 4 black balls one by one without replacement. Find the probability that both the balls are of different colours.
- a)1/7
- b)53/91
- c)3/14
- d)73/91
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Two balls are drawn at random from a bag containing 3 white, 3 red, 4 ...
Understanding the Problem
In the bag, we have:
- 3 White balls
- 3 Red balls
- 4 Green balls
- 4 Black balls
Total balls = 3 + 3 + 4 + 4 = 14 balls
We want to find the probability that both balls drawn are of different colors.
Total Ways to Draw Two Balls
The total number of ways to choose 2 balls from 14 is given by the combination formula:
- Total ways = 14C2 = (14 × 13) / (2 × 1) = 91
Calculating Favorable Outcomes
To find the favorable outcomes (where both balls are of different colors), we can calculate the total outcomes of choosing balls of the same color and subtract from the total outcomes.
Same Color Outcomes
1. White Balls:
- Ways to choose 2 white = 3C2 = 3
2. Red Balls:
- Ways to choose 2 red = 3C2 = 3
3. Green Balls:
- Ways to choose 2 green = 4C2 = 6
4. Black Balls:
- Ways to choose 2 black = 4C2 = 6
Total Same Color Outcomes
Total same color = 3 + 3 + 6 + 6 = 18
Calculating Different Color Outcomes
Favorable outcomes (different colors) = Total outcomes - Same color outcomes
- Different color outcomes = 91 - 18 = 73
Probability Calculation
The probability that both balls are of different colors is:
- Probability = Favorable outcomes / Total outcomes = 73 / 91
Thus, the correct answer is option D: 73/91.
In the bag, we have:
- 3 White balls
- 3 Red balls
- 4 Green balls
- 4 Black balls
Total balls = 3 + 3 + 4 + 4 = 14 balls
We want to find the probability that both balls drawn are of different colors.
Total Ways to Draw Two Balls
The total number of ways to choose 2 balls from 14 is given by the combination formula:
- Total ways = 14C2 = (14 × 13) / (2 × 1) = 91
Calculating Favorable Outcomes
To find the favorable outcomes (where both balls are of different colors), we can calculate the total outcomes of choosing balls of the same color and subtract from the total outcomes.
Same Color Outcomes
1. White Balls:
- Ways to choose 2 white = 3C2 = 3
2. Red Balls:
- Ways to choose 2 red = 3C2 = 3
3. Green Balls:
- Ways to choose 2 green = 4C2 = 6
4. Black Balls:
- Ways to choose 2 black = 4C2 = 6
Total Same Color Outcomes
Total same color = 3 + 3 + 6 + 6 = 18
Calculating Different Color Outcomes
Favorable outcomes (different colors) = Total outcomes - Same color outcomes
- Different color outcomes = 91 - 18 = 73
Probability Calculation
The probability that both balls are of different colors is:
- Probability = Favorable outcomes / Total outcomes = 73 / 91
Thus, the correct answer is option D: 73/91.
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Two balls are drawn at random from a bag containing 3 white, 3 red, 4 green and 4 black balls one by one without replacement. Find the probability that both the balls are of different colours.a)1/7b)53/91c)3/14d)73/91Correct answer is option 'D'. Can you explain this answer?
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