In a large school, it was found that 77% of students are taking a math class, 74% of student are taking an English class, and 70% of students are taking both. Find the probability that a randomly selected student is taking a math class or an English class. Write your answer as a decimal, and round to 2 decimal places if necessary. Find the probability that a randomly selected student is taking neither a math class nor an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.

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joaobezerra joaobezerra · Answer 1 · 2021-02-13T01:14:58+01:00

Answer:

0.81 = 81% probability that a randomly selected student is taking a math class or an English class.

0.19 = 19% probability that a randomly selected student is taking neither a math class nor an English class

Step-by-step explanation:

We solve this question working with the probabilities as Venn sets.

I am going to say that:

Event A: Taking a math class.

Event B: Taking an English class.

77% of students are taking a math class

This means that [tex]P(A) = 0.77[/tex]

74% of student are taking an English class

This means that [tex]P(B) = 0.74[/tex]

70% of students are taking both

This means that [tex]P(A \cap B) = 0.7[/tex]

Find the probability that a randomly selected student is taking a math class or an English class.

This is [tex]P(A \cup B)[/tex], which is given by:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

So

[tex]P(A \cup B) = 0.77 + 0.74 - 0.7 = 0.81[/tex]

0.81 = 81% probability that a randomly selected student is taking a math class or an English class.

Find the probability that a randomly selected student is taking neither a math class nor an English class.

This is

[tex]1 - P(A \cup B) = 1 - 0.81 = 0.19[/tex]

0.19 = 19% probability that a randomly selected student is taking neither a math class nor an English class