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A basket contains three blue and four red balls. If three balls are drawn at random from the basket, what is the probability that all the three balls are either blue or red?
  • a)
    1  
  • b)
    1 / 7
  • c)
    3 / 14  
  • d)
    3 / 28
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A basket contains three blue and four red balls. If three balls are dr...
Problem: A basket contains three blue and four red balls. If three balls are drawn at random from the basket, what is the probability that all the three balls are either blue or red?

Solution:

Total number of ways to draw 3 balls out of 7 = 7C3 (7 choose 3)

= 35

Number of ways to draw 3 blue balls out of 3 = 3C3 (3 choose 3)

= 1

Number of ways to draw 3 red balls out of 4 = 4C3 (4 choose 3)

= 4

Therefore, the total number of ways to draw 3 balls that are either blue or red = 1 + 4

= 5

Therefore, the probability of drawing 3 balls that are either blue or red = (Number of ways to draw 3 balls that are either blue or red) / (Total number of ways to draw 3 balls out of 7)

= 5 / 35

= 1 / 7

Hence, the correct option is (b) 1/7.
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Community Answer
A basket contains three blue and four red balls. If three balls are dr...
3B+4R~3c3+4c3 chances
total chances~7c3
so probability is5/35=1/7
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A basket contains three blue and four red balls. If three balls are drawn at random from the basket, what is the probability that all the three balls are either blue or red?a)1b)1 / 7c)3 / 14d)3 / 28Correct answer is option 'B'. Can you explain this answer?
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