shiladitya Posted June 4, 2015 Share Posted June 4, 2015 From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. What is the probability that Andrew will be among the 4 volunteers selected and Karen will not? a) 3/7 b) 5/12 c) 27/70 d)2/7 e) 9/35 Answer : c) 2/7 Quote Link to comment Share on other sites More sharing options...
Tristar Posted June 5, 2015 Share Posted June 5, 2015 Answer: 4 people can be selected out of 8 people in 8C4 ways = 70 (total number of cases). Assuming that Andrew is among the 4 volunteers selected, we have 3 remaining spots for 6 candidates (as Karen can't be on the same team as Andrew we do not consider her as a candidate for the first team). Now, 3 people can be selected out of 6 candidates in 6C3 ways = 20 (favorable number of cases). Our required probability P = Favorable Number of Cases / Total Number of Cases = 20/70 = 2/7. Quote Link to comment Share on other sites More sharing options...
Brent Hanneson Posted July 23, 2015 Share Posted July 23, 2015 From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. What is the probability that Andrew will be among the 4 volunteers selected and Karen will not? a) 3/7 b) 5/12 c) 27/70 d)2/7 e) 9/35 P(Andrew is selected but Karen is not selected) = (number of 4-person groups with Andrew but not Karen)/(total # of 4-person groups possible) number of 4-person groups with Andrew but not Karen Take the task of creating groups and break it into stages. Stage 1: Place Andrew in the 4-person group We can complete this stage in 1 way Stage 2: Send Karen out of the room and, from the remaining 6 volunteers, select 3 more people. Since the order in which we select the 3 volunteers does not matter, we can use combinations. We can select 3 people from 6 volunteers in 6C3 ways (20 ways). By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a 4-person group) in (1)(20) ways (= 20 ways) total # of 4-person groups possible We can select 4 people from all 8 volunteers in 8C4 ways ( = 70 ways). So, P(Andrew is selected but Karen is not selected) = (20)/(70) = 2/7 Cheers, Brent - GMAT Prep Now Quote Link to comment Share on other sites More sharing options...
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