recategorized by
8,434 views
20 votes
20 votes

A bag contains $10$ white balls and $15$ black balls. Two balls are drawn in succession. The probability that one of them is black and the other is white is:

  1. $\frac{2}{3}$

  2. $\frac{4}{5}$

  3. $\frac{1}{2}$

  4. $\frac{1}{3}$

recategorized by

6 Answers

Best answer
39 votes
39 votes

Answer is C

  • Probability of first ball white and second one black $=\left(\dfrac{10}{25}\right)\times \left(\dfrac{15}{24}\right)$
  • Probability of first ball black and second one white$=\left(\dfrac{15}{25}\right)\times \left(\dfrac{10}{24}\right)$
  • Probability $=$ sum of above two probabilities $=\dfrac{1}{2}.$
edited by
11 votes
11 votes
SInce 2 balls are drawn, sample space S = 2^2 = {BB,WW,BW,WB}

Probability that we get one of balck and one of white = (BW,WB)/S = 2/4 = 1/2

Answer : (c)
4 votes
4 votes
Probability that both balls are black=  (15C2)/(25C2) =7/20

Probability that both balls are white=  (10C2)/(25C2) =6/40

Probability that (both balls are black) or (both balls are white)= 7/20 + 6/40 =20/40=1/2

The probability that one of them is black and the other is white is: 1- 1/2 = 1/2
Answer:

Related questions

14 votes
14 votes
5 answers
1
gatecse asked Sep 15, 2014
10,999 views
The probability that a number selected at random between $100$ and $999$ (both inclusive) will not contain the digit $7$ is: $\dfrac{16}{25}$$\left(\dfrac{9}{10}\right)^...
44 votes
44 votes
1 answer
3
23 votes
23 votes
2 answers
4
Kathleen asked Oct 8, 2014
10,679 views
A computer system has a $4 \ K$ word cache organized in block-set-associative manner with $4$ blocks per set, $64$ words per block. The number of bits in the SET and WORD...