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In a certain Algebra 2 class of 30 students, 19 of them play basketball and 12 of them play baseball. There are 8 students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?

User Zuguang Gu
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1 Answer

4 votes

Answer:

Probability that a student chosen randomly from the class plays basketball or baseball is
(23)/(30) or 0.76

Explanation:

Given:

Total number of students in the class = 30

Number of students who plays basket ball = 19

Number of students who plays base ball = 12

Number of students who plays base both the games = 8

To find:

Probability that a student chosen randomly from the class plays basketball or baseball=?

Solution:


P(A \cup B)=P(A)+P(B)-P(A \cap B)---------------(1)

where

P(A) = Probability of choosing a student playing basket ball

P(B) = Probability of choosing a student playing base ball

P(A \cap B) = Probability of choosing a student playing both the games

Finding P(A)

P(A) =
\frac{\text { Number of students playing basket ball }}{\text{Total number of students}}

P(A) =
(19)/(30)--------------------------(2)

Finding P(B)

P(B) =
\frac{\text { Number of students playing baseball }}{\text{Total number of students}}

P(B) =
(12)/(30)---------------------------(3)

Finding
P(A \cap B)

P(A) =
\frac{\text { Number of students playing both games }}{\text{Total number of students}}

P(A) =
(8)/(30)-----------------------------(4)

Now substituting (2), (3) , (4) in (1), we get


P(A \cup B)= (19)/(30) + (12)/(30) -(8)/(30)


P(A \cup B)= (31)/(30) -(8)/(30)


P(A \cup B)= (23)/(30)

User Irwene
by
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