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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## When 2 people are selected at random from a group of 4 femal tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 1 member reply ### GMAT/MBA Expert ## When 2 people are selected at random from a group of 4 femal ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] When 2 people are selected at random from a group of 4 females and 4 males, what is the probability that at least one female is selected? A. 5/14 B. 7/14 C. 9/14 D. 11/14 E. 13/14 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$99 for 3 month Online Course
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Total possibilities 8c2 = (8*7)/2 = 28.

Now, since we are interested in probability at least one is female, we can find the probability that all 2 are males 4c2 = (4*3)/2 = 6.

Now 6/28 = 3/14.

The probability of at least one female = 1 - (3/14) = 11/14.

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The probability that at least one female is selected is equal to 1 minus the probability that two males are selected.
There are 4C2 ways of selecting 2 males from the four males and 8C2 ways of selecting 2 people from the group of 8. Therefore, the probability of selecting two males from the group is 4C2/8C2, and the probability of selecting at least one female is
1 - 4C2/8C2 = 1 - { (4*3)/(1*2) } / { (8*7)/(1*2) } = 1 - (4*3)/(8*7) = 1 - 3/14 = 11/14

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Only $99 for 3 month Online Course Free Resources-30 day online access & Diagnostic Test Unlimited Access to over 120 free video lessons-try it yourself Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1649 messages Followed by: 14 members Upvotes: 43 Max@Math Revolution wrote: When 2 people are selected at random from a group of 4 females and 4 males, what is the probability that at least one female is selected? A. 5/14 B. 7/14 C. 9/14 D. 11/14 E. 13/14 We can use the formula: P(at least one female is selected) = 1 - P(no females are selected) P(no females are selected) = 4/8 x 3/7 = 1/2 x 3/7 = 3/14 P(at least one female is selected) = 1 - 3/14 = 11/14. Alternate Solution: Without any restriction, there are 8C2 = 8!/(2!*6!) = 28 different ways to choose two people from a group of eight. We use the following formula: #ways to choose two people = #ways where at least one female is selected + #ways where no female is selected Notice that since there are 4 men, there are 4C2 = 4!/(2!*2!) = 6 ways to choose two people where no female is selected. Thus, 28 - 6 = 22 of the choices include at least one female. Thus, the probability that at least one female is selected is 22/28 = 11/14. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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