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At an elite baseball camp, 60% of players can bat both right-handed and left-handed. If 25% of the players who bat left-handed do not bat right-handed, what is the probability that a player selected at random does not bat left-handed?

User Orch
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1 Answer

6 votes

Answer:

The probability that a player selected at random does not bat left-handed is 20%.

Explanation:

Assume that there are a total of 100 baseball players at an elite baseball camp.

The information provided is:

  • 60% of players can bat both right-handed and left-handed.
  • 25% of the players who bat left-handed do not bat right-handed.

That is, the number of players can bat both right-handed and left-handed is,

n (L and R) = 60.

Now, if 25% of the players who bat left-handed do not bat right-handed, then 75% of all left-handed players can also bat right-handed.

⇒ n (L and R) = n (L) × 75%

60 = n (L) × 0.75

n (L) = 60/0.75

n (L) = 80

So there are 80 left handed batters.

Compute the number of only left handed batters as follows:

n (Only L) = n (L) × 25%

= 80 × 0.25

= 20

So there are 20 only left handed batters.

Compute the number of only right handed batters as follows:

Total = n (Only L) + n (Only R) + n (L and R)

100 = 20 + n (Only R) + 60

n (Only R) = 20

Thus, the probability that a player selected at random does not bat left-handed is 20%.

User Somrlik
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