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# When 2 people are selected at random from a group of 4 females and 4 m

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8005
GMAT 1: 760 Q51 V42
GPA: 3.82
When 2 people are selected at random from a group of 4 females and 4 m  [#permalink]

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28 Sep 2018, 00:42
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Difficulty:

15% (low)

Question Stats:

73% (01:07) correct 27% (02:02) wrong based on 57 sessions

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[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?

$$A. \frac{5}{14}$$
$$B. \frac{7}{14}$$
$$C. \frac{9}{14}$$
$$D. \frac{11}{14}$$
$$E. \frac{13}{14}$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 19 Oct 2013 Posts: 519 Location: Kuwait GPA: 3.2 WE: Engineering (Real Estate) When 2 people are selected at random from a group of 4 females and 4 m [#permalink] ### Show Tags 28 Sep 2018, 00:51 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 Probability of at least one female = 1 - (3/14) = 11/14 Answer choice D Posted from my mobile device CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2974 Location: India GMAT: INSIGHT Schools: Darden '21 WE: Education (Education) Re: When 2 people are selected at random from a group of 4 females and 4 m [#permalink] ### Show Tags 28 Sep 2018, 00:54 MathRevolution wrote: [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? $$A. \frac{5}{14}$$ $$B. \frac{7}{14}$$ $$C. \frac{9}{14}$$ $$D. \frac{11}{14}$$ $$E. \frac{13}{14}$$ Probability of 1 Female in selected team = 1- Probability of NO Female in selected team Probability of NO Female in selected team = 4C2/8C2 = 6/28 = 3/14 i.e. Probability of Atleast 1 female = 1-(3/14) = 11/14 Answer: Option D ALTERNATIVE Probability of atleast 1 female in team = Probability of exactly 1 female + probability of exactly two female = [(4C1*4C1)+(4C2)] / 8C2 = (16+6)/28 = 22/28 = 11/14 Answer: Option D _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8005 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: When 2 people are selected at random from a group of 4 females and 4 m [#permalink] ### Show Tags 30 Sep 2018, 22:58 => 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$$= 1 – { \frac{(4*3)}{(1*2) } / { (8*7)/(1*2)} } = 1 – \frac{(4*3)}{(8*7)} = 1 – \frac{3}{14} = \frac{11}{14}$$ Therefore, the answer is D. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: When 2 people are selected at random from a group of 4 females and 4 m   [#permalink] 30 Sep 2018, 22:58
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