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?

Step-by-step explanation:

Data given

Infielders: Outfielders = 7:4

Pitchers:Outfielders= 5:3

We can find a ratio in common for the 3 cases and in order to do this we can put the ratio with the same denominator of outfielders and we can do this:

Infielders:Outfielders x3 = 7:4 *3 = 21:12

Pitchers:Outfielders x4= 5:3 *4 = 15:12

And we have a one combined ratio:

Infielders:Outfielders:Pitchers = 21:12:20

And we have a basis or a total of 21+12+20 =53

And then we can find the probability that we select a pitcher like this: