A bag contains 7 green and 5 black balls. Three balls are drawn one after the other. The probability of all three balls being green, if the balls drawn are not replaced will be:
A) 123/897 B) 23/67 C) 7/44 D) 12/45
Answers
Answer:
7/44
Step-by-step explanation:
Answer: C) 7/44
Explanation:
Here, n(E) = 7C1×5C1×5C1
And, n(S) = 12C1*11C1*10C1
P(S) = 7*6*512*11*10 = 7/44
Given,
The total green balls = 7
The total black balls = 5
To Find,
The probability of all three balls being green, if the balls are not replaced=?
Solution,
Total balls in the bag = 5 + 7 = 12
The balls are not replaced which means each time the number of balls reduces by 1.
The total ways = 12C1*11C1*10C1
The total ways = 12 * 11 * 10
The total ways = 1320
The total ways of choosing 3 green balls = 7C1*6C1*5C1
The total ways of choosing 3 green balls = 7 * 6 * 5
The total ways of choosing 3 green balls = 210
Probability = 210 / 1320
Probability = 7 / 44
Hence, the probability of all three balls being green, if the balls are not replaced is 7/44. Option(c) is the correct answer.