21 votes 21 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: $\frac{2}{3}$ $\frac{4}{5}$ $\frac{1}{2}$ $\frac{1}{3}$ Probability gate1995 probability normal + – Kathleen asked Oct 8, 2014 • recategorized Apr 25, 2021 by Lakshman Bhaiya Kathleen 8.6k views answer comment Share Follow See 1 comment See all 1 1 comment reply Nit9 commented Nov 9, 2017 i edited by Nit9 Nov 9, 2017 reply Follow Share Two balls are drawn in succession, = without replacement, 7 votes 7 votes Please log in or register to add a comment.
Best answer 42 votes 42 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 $=\dfrac{1}{2}.$ ankitrokdeonsns answered Oct 24, 2014 • edited Sep 25, 2018 by Krithiga2101 ankitrokdeonsns comment Share Follow See all 2 Comments See all 2 2 Comments reply talha hashim commented Jul 25, 2018 reply Follow Share (10C1 * 15C1)/(25C2)=0.5(hypergeometric distribution) 23 votes 23 votes Vandit Shah commented Sep 21, 2021 reply Follow Share 👌 👍 0 votes 0 votes Please log in or register to add a comment.
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) Pronomita Dey 1 answered Dec 28, 2017 Pronomita Dey 1 comment Share Follow See all 2 Comments See all 2 2 Comments reply ayush.5 commented Mar 28, 2019 reply Follow Share So according to you, if there are 25 white balls and 15 black ,then also ans will be 1/2 ? 0 votes 0 votes Paatni22 commented Dec 28, 2020 reply Follow Share yes this is not the right way to do here 1 votes 1 votes Please log in or register to add a comment.
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 Sourav Basu answered Nov 4, 2017 Sourav Basu comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes Probability = (10C1 * 15C1)/25C2 manikantsharma answered Jun 17, 2020 manikantsharma comment Share Follow See all 0 reply Please log in or register to add a comment.