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A bag contains 14 red and 6 white balls. Two balls are drawn at random. What is the probability that they are of the same color?
- a)53/95
- b)23/67
- c)47/90
- d)25/37
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A bag contains 14 red and 6 white balls. Two balls are drawn at rando...
Number of sample space= 20C2= 190
Number of events= 14C2 + 6C2 = 14×13/2 + 6× 5/2= 91+15= 106
Required probability= 106/190= 53/95
Number of sample space= 20C2= 190
Number of events= 14C2 + 6C2 = 14×13/2 + 6× 5/2= 91+15= 106
Required probability= 106/190= 53/95
Most Upvoted Answer
A bag contains 14 red and 6 white balls. Two balls are drawn at rando...
Problem
A bag contains 14 red and 6 white balls. Two balls are drawn at random. What is the probability that they are of the same color?
Solution
The total number of ways in which we can draw 2 balls from 20 balls is 20C2 = (20 × 19) / (2 × 1) = 190.
Let's calculate the probability that we draw 2 red balls. The total number of ways in which we can draw 2 red balls from 14 red balls is 14C2 = (14 × 13) / (2 × 1) = 91. Therefore, the probability of drawing 2 red balls is:
P(Red,Red) = 91 / 190
Similarly, the probability of drawing 2 white balls is:
P(White,White) = 6C2 / 20C2 = (6 × 5) / (20 × 19) = 15 / 190
Therefore, the probability of drawing 2 balls of the same color is:
P(Same Color) = P(Red,Red) + P(White,White) = 91 / 190 + 15 / 190 = 106 / 190 = 53 / 95
Therefore, the correct option is (A).
Answer: (A) 53/95
A bag contains 14 red and 6 white balls. Two balls are drawn at random. What is the probability that they are of the same color?
Solution
The total number of ways in which we can draw 2 balls from 20 balls is 20C2 = (20 × 19) / (2 × 1) = 190.
Let's calculate the probability that we draw 2 red balls. The total number of ways in which we can draw 2 red balls from 14 red balls is 14C2 = (14 × 13) / (2 × 1) = 91. Therefore, the probability of drawing 2 red balls is:
P(Red,Red) = 91 / 190
Similarly, the probability of drawing 2 white balls is:
P(White,White) = 6C2 / 20C2 = (6 × 5) / (20 × 19) = 15 / 190
Therefore, the probability of drawing 2 balls of the same color is:
P(Same Color) = P(Red,Red) + P(White,White) = 91 / 190 + 15 / 190 = 106 / 190 = 53 / 95
Therefore, the correct option is (A).
Answer: (A) 53/95
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A bag contains 14 red and 6 white balls. Two balls are drawn at random. What is the probability that they are of the same color?a)53/95b)23/67c)47/90d)25/37Correct answer is option 'A'. Can you explain this answer?
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