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A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour is
- a)1/15
- b)2/5
- c)4/15
- d)7/15
Correct answer is option 'D'. Can you explain this answer?
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A bag contains 6 white and 4 black balls. Two balls are drawn at rando...
Probability of Drawing Two Balls of the Same Color
To calculate the probability of drawing two balls of the same color from the bag containing 6 white and 4 black balls, we need to consider the total number of ways to draw two balls and the number of ways to draw two balls of the same color.
Total Number of Ways to Draw Two Balls
- Total number of balls = 6 white + 4 black = 10
- Number of ways to draw the first ball = 10
- Number of ways to draw the second ball = 9 (since one ball has already been drawn)
- Total number of ways to draw two balls = 10 * 9 = 90
Number of Ways to Draw Two Balls of the Same Color
- Number of ways to draw two white balls = 6 * 5 = 30
- Number of ways to draw two black balls = 4 * 3 = 12
- Total number of ways to draw two balls of the same color = 30 (white) + 12 (black) = 42
Calculating the Probability
- Probability of drawing two balls of the same color = Number of ways to draw two balls of the same color / Total number of ways to draw two balls
- Probability = 42 / 90 = 7 / 15
Therefore, the probability that two balls drawn from the bag are of the same color is 7/15.
To calculate the probability of drawing two balls of the same color from the bag containing 6 white and 4 black balls, we need to consider the total number of ways to draw two balls and the number of ways to draw two balls of the same color.
Total Number of Ways to Draw Two Balls
- Total number of balls = 6 white + 4 black = 10
- Number of ways to draw the first ball = 10
- Number of ways to draw the second ball = 9 (since one ball has already been drawn)
- Total number of ways to draw two balls = 10 * 9 = 90
Number of Ways to Draw Two Balls of the Same Color
- Number of ways to draw two white balls = 6 * 5 = 30
- Number of ways to draw two black balls = 4 * 3 = 12
- Total number of ways to draw two balls of the same color = 30 (white) + 12 (black) = 42
Calculating the Probability
- Probability of drawing two balls of the same color = Number of ways to draw two balls of the same color / Total number of ways to draw two balls
- Probability = 42 / 90 = 7 / 15
Therefore, the probability that two balls drawn from the bag are of the same color is 7/15.
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A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour isa)1/15b)2/5c)4/15d)7/15Correct answer is option 'D'. Can you explain this answer?
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