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A bag contains 6 blue balls and 4 black balls. If two balls are selected at random, what is the probability that both are black?
- a)4/15
- b)2/15
- c)7/17
- d)2/17
- e)5/21
Correct answer is option 'B'. Can you explain this answer?
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A bag contains 6 blue balls and 4 black balls. If two balls are select...
Problem: A bag contains 6 blue balls and 4 black balls. If two balls are selected at random, what is the probability that both are black?
Solution:
Total number of balls in the bag = 6 blue + 4 black = 10
Number of ways to select 2 balls out of 10 = 10C2 = (10*9)/(2*1) = 45
Number of ways to select 2 black balls out of 4 = 4C2 = (4*3)/(2*1) = 6
Therefore, the probability of selecting 2 black balls = Number of ways to select 2 black balls / Number of ways to select 2 balls
= 6/45
= 2/15
Hence, the correct option is (B) 2/15.
Solution:
Total number of balls in the bag = 6 blue + 4 black = 10
Number of ways to select 2 balls out of 10 = 10C2 = (10*9)/(2*1) = 45
Number of ways to select 2 black balls out of 4 = 4C2 = (4*3)/(2*1) = 6
Therefore, the probability of selecting 2 black balls = Number of ways to select 2 black balls / Number of ways to select 2 balls
= 6/45
= 2/15
Hence, the correct option is (B) 2/15.
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