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On a county-wide baseball team, the best players were sent f

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On a county-wide baseball team, the best players were sent f [#permalink] New post 18 Apr 2020, 08:53
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79% (01:26) correct 20% (01:59) wrong based on 24 sessions
On a county-wide baseball team, the best players were sent from each high school. There are three mutually exclusive categories of players on this team: infielders, outfielders, and pitchers. If the ratio of infielders to outfielders is 7:4, and the ratio of pitchers to outfielders is 5:3, then if we pick one player at random from the county-wide baseball team, what is the probability that we will pick a pitcher?

A) \(\frac{1}{3}\)

B) \(\frac{4}{13}\)

C) \(\frac{5}{16}\)

D) \(\frac{20}{33}\)

E) \(\frac{20}{53}\)
[Reveal] Spoiler: OA
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Re: On a county-wide baseball team, the best players were sent f [#permalink] New post 18 Apr 2020, 09:37
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it is combined ratio question.
infielders to outfielders is 7:4, and the ratio of pitchers to outfielders is 5:3
so
infielders : outfielders : outfielders
7 : 4
3 : 5
so combined ratio is 3*(7:4 )and 4(3:5)
infielders : outfielders : outfielders
21 : 12 : 20
total =53
so probability of selecting outfielders=20/53
E
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Re: On a county-wide baseball team, the best players were sent f [#permalink] New post 19 Apr 2020, 00:06
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Ratio of infielders to outfielders = 7: 4
Multiplying this ratio by 3 we get = (7 *3) : (4 * 3) = 21 : 12
Ratio of pitchers to outfielders = 5 : 3
Multiplying this ratio by 4 we get = (5 * 4) : (3 * 4) = 20 : 12
Combining both the ratio since outfielder number is common , hence ratio of outfielders to infielder to pitchers = 12: 21: 20

Probability of picking a pitcher from this team = Number of pitchers / Total members in the team = 20 / (20 + 21 +12)
= 20 /53

Answer is E
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Re: On a county-wide baseball team, the best players were sent f [#permalink] New post 05 Jul 2020, 03:48
On a county-wide baseball team, the best players were sent from each high school. There are three mutually exclusive categories of players on this team: infielders, outfielders, and pitchers. If the ratio of infielders to outfielders is 7:4, and the ratio of pitchers to outfielders is 5:3, then if we pick one player at random from the county-wide baseball team, what is the probability that we will pick a pitcher?

Its a combined ratio problem:
In:Out:Pit
7:4:__
_:3:5

Now we will multiply ratios with the ratio of outfielders since it is common in both
3(7:4) = 21:12
and
4(3:5) = 12:20

Now,
In:Out:Pit
21:12:__
_:12:20

Total = 21+12+20 = 53
pitcher / total = 20/53 which is option E
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Re: On a county-wide baseball team, the best players were sent f   [#permalink] 05 Jul 2020, 03:48
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On a county-wide baseball team, the best players were sent f

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