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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