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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... tagged by: swerve ##### This topic has 1 expert reply and 1 member reply ### Top Member ## In a certain game, you perform three tasks. you flip a... 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 exactly one of these three tasks is 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 The OA is E. Please, can any expert explain this PS question for me? I can't get the correct answer. I need your help. Thanks. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 swerve 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 exactly one of these three tasks is 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 The OA is E. Please, can any expert explain this PS question for me? I can't get the correct answer. I need your help. Thanks. This is a very strange game, indeed. So the idea is that you "win" if exactly one of the three contests is a success. Meaning: there are three ways you can win. 1) Coin = success/ die = fail / card = fail - 2) Coin = Fail / Die = success / card = Fail 3) Coin = Fail/Die =fail / card = success Bearing in mind that a coin flip brings a 1/2 probability of success, the die roll brings a 1/6 probability of success (and a 5/6 probability of failure); and the card pick brings a 1/4 probability of success (and a 3/4 probability of failure,) let's evaluate each in turn 1) Coin = success/ die = fail / card = fail ---> (1/2)(5/6)(3/4) = 15/48 2) Coin = Fail / Die = success / card = Fail ---> (1/2)(1/6)(3/4) = 3/48 3) Coin = Fail/Die =fail / card = success --->(1/2)(5/6)(1/4) = 5/48 Add 'em up (15/48) + (3/48) + (5/48) = 23/48. The answer is E _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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Probability of winning= probability that only one of the three tasks is successful
(i) flipping a quarter (heads - success)--- (A)
prob. of success (A)=1/2, probability of losing (A)=1/2

(ii) rolling a single die, (six-success)--- (B)
prob. of success (B) = 1/6, prob of losing (B)=5/6

(iii) picking a card from a desk (spades-success)----(C)
prob. of success (C) =13/52 =1/4, probability of losing (C)= 1 - (1/4) = 3/4

$$probability\ of\ winning=A\ B.C.\ +A.\ B\ C.+A.B.\ C$$
$$=\left(\frac{1}{2}\cdot\frac{5}{6}\cdot\frac{3}{4}\right)+\left(\frac{1}{2}\cdot\frac{1}{6}\cdot\frac{3}{4}\right)+\left(\frac{1}{2}\cdot\frac{5}{6}\cdot\frac{1}{4}\right)$$
$$\frac{15}{48}+\frac{3}{48}+\frac{5}{48}=\frac{23}{48}\ \left(Option\ E\right)$$

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