3 votes 3 votes Two cards are drawn together from a pack of 52 cards, What is the probability that One is spade and other is king?? Aboveallplayer asked Aug 12, 2016 Aboveallplayer 686 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 5 votes 5 votes case 1 spade king and spade or non-spade king and spade (1/52 x 12/51 +3/52 x 13/51)=51/52 x51=1/52 case 2 spade x non spade king or spade and spade king (13/51 x 3/51 + 12/51 x 1/52) =51/52x51=1/52 total prob =1/52+1/52 =1/26 ans Sanjay Sharma answered Aug 12, 2016 selected Aug 13, 2016 by Aboveallplayer Sanjay Sharma comment Share Follow See 1 comment See all 1 1 comment reply Neelesh Pandey commented Sep 11, 2016 reply Follow Share what if both are same,ie,in only one attempt we get spade king and spade card too? 0 votes 0 votes Please log in or register to add a comment.
2 votes 2 votes Total sample space = 52C2 No. of spade = 13 No. of king = 4 so probability = (13 * 4 ) / 52C2 Prashant. answered Aug 12, 2016 edited Aug 12, 2016 by Prashant. Prashant. comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes With Replacement: $\frac{_{1}^{13}\textrm{C} *_{1}^{4}\textrm{C} }{_{1}^{52}\textrm{C} *_{1}^{52}\textrm{C} }$ Without Replacement: $\frac{(_{1}^{1}\textrm{C} *_{1}^{3}\textrm{C})+(_{1}^{12}\textrm{C}*_{1}^{4}\textrm{C})) }{_{2}^{52}\textrm{C} }$ srestha answered Aug 12, 2016 edited Aug 12, 2016 by srestha srestha comment Share Follow See all 6 Comments See all 6 6 Comments reply vijaycs commented Aug 12, 2016 reply Follow Share Since, cards are drawn together, so your second case should be ans here with little modification, that is denominator should be 50C2 ..I think ... @srestha .. please check it 2 votes 2 votes papesh commented Aug 12, 2016 reply Follow Share Yup.. 0 votes 0 votes Aboveallplayer commented Aug 12, 2016 reply Follow Share Okay, what should be the final answer like (in terms of expression, Not the exact answer) 0 votes 0 votes vijaycs commented Aug 12, 2016 reply Follow Share @udditpto , I think ans should be p= 1/26 ... 1 votes 1 votes srestha commented Aug 12, 2016 reply Follow Share yes and that case without replacement will be the answer @vijay 1 votes 1 votes vijaycs commented Aug 12, 2016 i edited by vijaycs Aug 12, 2016 reply Follow Share Yes @Srestha... :) And With replacement - $\frac{2*(12C2 * 4C1 + 1C1 * 3C1) +1}{52C1*52C1}$ where, 2* 12C2 * 4C1 - > In first throw its a spade but not king and in 2nd throw its a king and vice versa. 2 *1C1 *3C1 - > In first throw its a king without spade and in 2nd throw its a king with spade..and vice-versa. 1 - > In first throw its a king with spade and in 2nd throw its same card as first one. Check please.. 2 votes 2 votes Please log in or register to add a comment.