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A box contains 5 white, 4 green, 2 blue and 3 black marbles. If 2 marbles are drawn at random, what is the probability that both are green or at least one is green ?
- a)46/91
- b)32/97
- c)16/75
- d)1/54
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A box contains 5 white, 4 green, 2 blue and 3 black marbles. If 2 marb...
4C2+(4C1*10C1)/12C2 = 6+40/91 = 46/91
Most Upvoted Answer
A box contains 5 white, 4 green, 2 blue and 3 black marbles. If 2 marb...
Problem Statement:
A box contains 5 white, 4 green, 2 blue and 3 black marbles. If 2 marbles are drawn at random, what is the probability that both are green or at least one is green?
Solution:
Total number of marbles in the box = 5 + 4 + 2 + 3 = 14
Number of ways to select 2 marbles from 14 = 14C2 = 91
Number of ways to select 2 green marbles from 4 green marbles = 4C2 = 6
Number of ways to select 1 green marble and 1 non-green marble = (4C1 x 10C1) = 40
Number of ways to select 2 non-green marbles = 10C2 = 45
Therefore, the probability of selecting 2 green marbles = 6/91
The probability of selecting at least one green marble can be calculated as follows:
Probability of selecting 1 green marble and 1 non-green marble + Probability of selecting 2 green marbles
= (40/91) + (6/91)
= 46/91
Therefore, the required probability is 46/91.
Answer: a) 46/91
A box contains 5 white, 4 green, 2 blue and 3 black marbles. If 2 marbles are drawn at random, what is the probability that both are green or at least one is green?
Solution:
Total number of marbles in the box = 5 + 4 + 2 + 3 = 14
Number of ways to select 2 marbles from 14 = 14C2 = 91
Number of ways to select 2 green marbles from 4 green marbles = 4C2 = 6
Number of ways to select 1 green marble and 1 non-green marble = (4C1 x 10C1) = 40
Number of ways to select 2 non-green marbles = 10C2 = 45
Therefore, the probability of selecting 2 green marbles = 6/91
The probability of selecting at least one green marble can be calculated as follows:
Probability of selecting 1 green marble and 1 non-green marble + Probability of selecting 2 green marbles
= (40/91) + (6/91)
= 46/91
Therefore, the required probability is 46/91.
Answer: a) 46/91
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