PrepRung
Sign inSign up free

NDA 2020 Maths · Mathematics · Probability · medium

A box contains 4 white and 6 black balls. Three balls are drawn at random without replacement. The probability that exactly two are white is

Single correct option

A box contains 44 white and 66 black balls. Three balls are drawn at random without replacement. The probability that exactly two are white is
  1. A. 36125\dfrac{36}{125}
  2. B. 310\dfrac{3}{10}
  3. C. 15\dfrac15
  4. D. 25\dfrac25
Show answer and solution

Answer: (B) 310\dfrac{3}{10}

Favourable ways: (42)(61)=6⋅6=36\binom42\binom61=6\cdot6=36, total ways (103)=120\binom{10}{3}=120, so the probability is 36120=310\dfrac{36}{120}=\dfrac3{10}. The value 36125\dfrac{36}{125} is the answer if the balls were drawn with replacement, 3(25)2353\left(\dfrac25\right)^2\dfrac35, which the word \"without replacement\" excludes. Choosing the two white balls and the black ball in separate stages and ordering them also gives 310\dfrac{3}{10}.
Report a mistake

Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake