Probability - Arithmetic Aptitude Questions and Answers

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A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

\(\frac { 1 } { 22 } \)

\(\frac { 3 } { 22 } \)

\(\frac { 2 } { 21 }\)

\(\frac { 2 } {77 } \)

Answer : Option C

Explanation :

Let S be the sample space.

Then, n(S)	= number of ways of drawing 3 balls out of 15
	= ¹⁵C₃

= \(\frac { (15*14*13) } { (3*2*1) }\)

= 455

Let E = event of getting all the 3 red balls.

n(E) = ⁵C₃ = ⁵C₂ =\(\frac { (5*1) } { (2 *1)} \)=10

P(E) =\(\frac { n(E) } { n(S)} \)=\( \frac { 10 } { 455 } \)=\(\frac { 2 } { 21 }\)