Probability Ques 24
Question-
In a bag there are 4 red balls, 2 green balls and 3 yellow balls. If two balls are drawn at random, what is the probability that at least one of the balls is green in colour?
(1) $\frac{7}{12}$
(2) $\frac{1}{4}$
(3) $\frac{5}{12}$
(4) $\frac{1}{6}$
(5) $\frac{1}{12}$
(IBPS SO (IT Officer) CWE (Prelim Exam) 30.12.2017)
Show Answer
Correct Answer: (3)
Solution: (3)
Total number of balls $=4+2+3=9$
Total possible outcomes $=$ Selection of 2 balls out of 9 balls $={ }^{9} C_{2}=\frac{9 \times 8}{1 \times 2}=36$
Favourable outcomes $=$ One green ball and the other yellow or red ball + both green balls $={ }^{2} C_{1} \times{ }^{7} C_{1}+{ }^{2} C_{2}$ $=2 \times 7+1=15$
Required probability $=\frac{15}{36}=\frac{5}{12}$
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