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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 ## In a certain game, you perform three tasks. You flip a quart ##### This topic has 2 expert replies and 0 member replies ### Top Member ## In a certain game, you perform three tasks. You flip a quart ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning? A. 1/48 B. 5/16 C. 11/12 D. 11/16 E. 23/48 OA D Source: Magoosh ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 866 messages Followed by: 26 members Upvotes: 59 BTGmoderatorDC wrote: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning? A. 1/48 B. 5/16 C. 11/12 D. 11/16 E. 23/48 Source: Magoosh $$\left. \matrix{ {\rm{i}}\,\,{\rm{:}}\,\,\,{\rm{get}}\,\,{\rm{H}}\,\,{\rm{in}}\,\,{\rm{quarter}} \hfill \cr {\rm{ii}}:\,\,{\rm{get}}\,\,6\,\,{\rm{in}}\,{\rm{die}} \hfill \cr {\rm{iii}}\,\,{\rm{:}}\,\,{\rm{get}}\,\,{\rm{spades}}\,{\rm{in}}\,{\rm{52}}\,\,{\rm{cards}}\,{\rm{regular}}\,\,{\rm{deck}} \hfill \cr} \right\}\,\,\,{\rm{independent}}\,\,{\rm{events}}\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{their}}\,\,{\rm{negations}}\,\,{\rm{are}}\,\,{\rm{independent}}\,\,{\rm{events}}\,\,\,\,\,\left( * \right)$$ $$? = P\left( {{\rm{i}}\,\,{\rm{OR}}\,\,{\rm{ii}}\,\,{\rm{OR}}\,\,{\rm{iii}}} \right) = 1 - P\left( {\left( {{\rm{not}}\,\,{\rm{i}}} \right)\,\,AND\,\,\left( {{\rm{not}}\,\,{\rm{ii}}} \right)\,\,AND\,\,\left( {{\rm{not}}\,\,{\rm{iii}}} \right)} \right)$$ $$P\left( {\left( {{\rm{not}}\,\,{\rm{i}}} \right)\,\,AND\,\,\left( {{\rm{not}}\,\,{\rm{ii}}} \right)\,\,AND\,\,\left( {{\rm{not}}\,\,{\rm{iii}}} \right)} \right)\,\,\mathop = \limits^{\left( * \right)} \,\,\,{1 \over 2} \cdot {5 \over 6} \cdot {{52 - 13} \over {52}} = {5 \over {16}}$$ $$? = 1 - {5 \over {16}} = {{11} \over {16}}$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version) Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1767 messages Followed by: 14 members Upvotes: 43 BTGmoderatorDC wrote: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning? A. 1/48 B. 5/16 C. 11/12 D. 11/16 E. 23/48 We can let A = event of getting heads when flipping the quarter, B = event of getting a six when rolling the die and C = event of getting a spades card, and use the following formula: P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C) P(A or B or C) = 1/2 + 1/6 + 1/4 - (1/2 x 1/6) - (1/2 x 1/4) - (1/4 x 1/6) + (1/2 x 1/6 x 1/4) P(A or B or C) = 11/12 - 1/12 - 1/8 - 1/24 + 1/48 P(A or B or C) = 11/16 Alternate Solution: We notice that P(success) + P(failure) = 1; therefore, P(success) = 1 - P(failure). Letâ€™s find P(failure). The only way we fail in this game is if we get tails from the quarter flip AND not get a six from the die roll AND not get a spade from the card draw. Therefore, P(failure) = 1/2 x 5/6 x 3/4 = 15/48 = 5/16 Thus, P(success) = 1 - P(failure) = 1 - 5/16 = 11/16 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 • FREE GMAT Exam Know how you'd score today for$0

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