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A bag contains 3 green and 7 white balls. Two balls are drawn from the bag in succession without replacement. What is the probability that
(i) they are of different colour?
  • a)
    7/15
  • b)
    7/9
  • c)
    5/11
  • d)
    7/11
Correct answer is option 'A'. Can you explain this answer?
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A bag contains 3 green and 7 white balls. Two balls are drawn from the...
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A bag contains 3 green and 7 white balls. Two balls are drawn from the...
Solution:
Given, a bag contains 3 green and 7 white balls.

Probability of drawing 1st ball:
P(Green) = 3/10
P(White) = 7/10

After drawing 1st ball, we have one less ball in the bag.
So, the probability of drawing 2nd ball changes.

If the 1st ball was green, then there are 2 green and 7 white balls left in the bag.
P(2nd ball is White | 1st ball was Green) = 7/9
P(2nd ball is Green | 1st ball was Green) = 2/9

If the 1st ball was white, then there are 3 green and 6 white balls left in the bag.
P(2nd ball is Green | 1st ball was White) = 3/9
P(2nd ball is White | 1st ball was White) = 6/9

(i) Probability that the two balls are of different colour:
P(1st ball is Green and 2nd ball is White) + P(1st ball is White and 2nd ball is Green)
= (3/10 x 7/9) + (7/10 x 3/9)
= 21/90 + 21/90
= 42/90
= 7/15

Therefore, the probability that the two balls are of different colour is 7/15.
Hence, option (a) is correct.
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A bag contains 3 green and 7 white balls. Two balls are drawn from the bag in succession without replacement. What is the probability that(i) they are of different colour?a)7/15b)7/9c)5/11d)7/11Correct answer is option 'A'. Can you explain this answer?
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